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#3-1 Chapter 3 for age 14// Teaching True Mathematics

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  #3-1  Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 18:50 -0700
    3-1 through 3-3 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 21:26 -0700
      3-4 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 21:41 -0700
        3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 22:19 -0700
          Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 01:46 -0700
            Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Earle Jones <earle.jones@comcast.net> - 2018-05-16 09:20 -0700
            Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 11:05 -0700
              better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 10:53 -0700
                Re: better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 11:10 -0700
                  These ideas belong in my other quest to unify Conic sections with Regular Polyhedra Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 16:06 -0700
                    Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:19 +0000
                Re: Archimedes "Failure" Plutonium flunks the lifelong Math test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-17 19:16 +0000
          3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 12:43 -0700
            Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 21:04 -0700
              Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:26 +0000
              Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 21:44 -0700
                Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:56 +0000
                Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-18 07:01 -0700
                  Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics True Mathematics Learner <francois.grondin2003@gmail.com> - 2018-05-19 11:44 -0700
                    Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-19 13:10 -0700
                      Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Alan Mackenzie <acm@muc.de> - 2018-05-21 09:18 +0000
          3-6, 3-7 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 22:31 -0700

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#413152 — #3-1 Chapter 3 for age 14// Teaching True Mathematics

Newsgroups: sci.math
Date: Sat, 21 Apr 2018 23:02:04 -0700 (PDT)

Subject: #3-1  Chapter 3 for age 14// Teaching True Mathematics
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sun, 22 Apr 2018 06:02:04 +0000

#3-1 Chapter 3 for age 14// Teaching True Mathematics

#3-1  Chapter 3 for age 14// Teaching True Mathematics 

Alright, you made it this far. Chapter 1 was all for the age 8 Grade School students. They had there very own chapter. Chapter 2 was for ages 9 to 13, and then chapter 3 is all for the age of 14 year olds. Ages 15 through 18 are for High School, freshman, sophomore, junior, senior. For freshman we want to do nothing but Geometry, for sophomore we want to do Algebra, for juniors we want Trigonometry, and for seniors PreCalculus. 

For 14 year olds, before they go to High School, we want to make sure they learned well all the lessons so far in this book, but not all is review, for we teach them Geometry-Logic which is Set theory with a spin. So, this chapter is about review, and then a new topic of Geometrical-Logic. 

We begin the review as we started the textbook,-- memorization of the multiplication table-- what is 54? Someone will blurt out 9*6, then ask, what is 56? Someone will blurt out 8*7. Ask what is 7*8? Ask what is 9*3 and then ask what is 2 of 9*3, and teach the students that if your memory fails you on 9*6, cut it in half to 9*3 = 27 and double it is 54. Same goes for 7*8 = 56, if you forget, cut it in half with 7*4 =28 and double 28 is 56. 

Teach the students to have a flexible alternative mind at solving, so you forget what 8*7 is, shaky if it is 54 or 56, so just cut it in half 4*7=28 and then you know 8*7 is 56. 

I used to love Dodge ball in High School, just loved that sport. Can we set up mathematics memorization of the Multiplication Table as a sort of Dodge Ball contest. But we must remember, some students are slow at memorizing and others fast, so we must never embarrass any student. Always have learning and teaching on a positive upward motivation. Never ever make fun or light of a student slow to learn. And the teacher has to guard and protect the slow learners. 

So, we review multiplication tables. Now review add and subtract decimals, and multiply with decimals. But the biggest review is Long Division. And on the first day of class, tell the students then must have two papers which they will be working in class and at home, for homework for several weeks. What they are going to do is learn something about Infinity and angles at infinity and about five beautiful objects in Nature-- the five regular-polyhedra. Teacher show them the dice. But now, show them two papers where the teacher has already done the homework exercise. 

Divide the below number of 603 digits by 12, where the division is done all on one side of a paper 
 31415926535 8979323846 2643383279 5028841971 6939937510 
 5820974944 5923078164 0628620899 8628034825 3421170679   
 8214808651 3282306647 0938446095 5058223172 5359408128 
 4811174502 8410270193 8521105559 6446229489 5493038196 
 4428810975 6659334461 2847564823 3786783165 2712019091 
 4564856692 3460348610 4543266482 1339360726 0249141273   
 7245870066 0631558817 4881520920 9628292540 9171536436 
 7892590360 0113305305 4882046652 1384146951 9415116094   
 3305727036 5759591953 0921861173 8193261179 3105118548 
 0744623799 6274956735 1885752724 8912279381 8301194912 
 9833673362 4406566430 8602139494 6395224737 1907021798   
 6094370277 0539217176 2931767523 8467481846 7669405132 
 00 

Now, after the above is done, on a second paper, both front and back divide by 72 this 1208 digit number 

 31415926535 8979323846 2643383279 5028841971 6939937510 
 5820974944 5923078164 0628620899 8628034825 3421170679   
 8214808651 3282306647 0938446095 5058223172 5359408128 
 4811174502 8410270193 8521105559 6446229489 5493038196 
 4428810975 6659334461 2847564823 3786783165 2712019091 
 4564856692 3460348610 4543266482 1339360726 0249141273   
 7245870066 0631558817 4881520920 9628292540 9171536436 
 7892590360 0113305305 4882046652 1384146951 9415116094   
 3305727036 5759591953 0921861173 8193261179 3105118548 
 0744623799 6274956735 1885752724 8912279381 8301194912 
 9833673362 4406566430 8602139494 6395224737 1907021798   
 6094370277 0539217176 2931767523 8467481846 7669405132 
 0005681271 4526356082 7785771342 7577896091 7363717872 
1468440901 2249534301 4654958537 1050792279 6892589235 
4201995611 2129021960 8640344181 5981362977 4771309960   
5187072113 4999999837 2978049951 0597317328 1609631859 
5024459455 3469083026 4252230825 3344685035 2619311881 
7101000313 7838752886 5875332083 8142061717 7669147303     
5982534904 2875546873 1159562863 8823537875 9375195778   
1857780532 1712268066 1300192787 6611195909 2164201989   
3809525720 1065485863 2788659361 5338182796 8230301952 
0353018529 6899577362 2599413891 2497217752 8347913151     
5574857242 4541506959 5082953311 6861727855 8890750983 
8175463746 4939319255 0604009277 0167113900 9848824012                               
8583616 

Of course, in both divisions the student needs to use the AP Long Division method where we subtract and carry over, not bring down. You have to do the Long Division by the AP method in order to use just one sheet of paper for each division, first by 12 then by 72.

Ask the 14 year old if the number looks vaguely familiar to anyone? 

AP

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#413170 — 3-1 through 3-3 Chapter 3 for age 14// Teaching True Mathematics

Newsgroups: sci.math
Date: Sat, 21 Apr 2018 23:02:04 -0700 (PDT)

Subject: #3-1  Chapter 3 for age 14// Teaching True Mathematics
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sun, 22 Apr 2018 06:02:04 +0000

#3-1 Chapter 3 for age 14// Teaching True Mathematics

#3-1  Chapter 3 for age 14// Teaching True Mathematics 

Alright, you made it this far. Chapter 1 was all for the age 8 Grade School students. They had there very own chapter. Chapter 2 was for ages 9 to 13, and then chapter 3 is all for the age of 14 year olds. Ages 15 through 18 are for High School, freshman, sophomore, junior, senior. For freshman we want to do nothing but Geometry, for sophomore we want to do Algebra, for juniors we want Trigonometry, and for seniors PreCalculus. 

For 14 year olds, before they go to High School, we want to make sure they learned well all the lessons so far in this book, but not all is review, for we teach them Geometry-Logic which is Set theory with a spin. So, this chapter is about review, and then a new topic of Geometrical-Logic. 

We begin the review as we started the textbook,-- memorization of the multiplication table-- what is 54? Someone will blurt out 9*6, then ask, what is 56? Someone will blurt out 8*7. Ask what is 7*8? Ask what is 9*3 and then ask what is 2 of 9*3, and teach the students that if your memory fails you on 9*6, cut it in half to 9*3 = 27 and double it is 54. Same goes for 7*8 = 56, if you forget, cut it in half with 7*4 =28 and double 28 is 56. 

Teach the students to have a flexible alternative mind at solving, so you forget what 8*7 is, shaky if it is 54 or 56, so just cut it in half 4*7=28 and then you know 8*7 is 56. 

I used to love Dodge ball in High School, just loved that sport. Can we set up mathematics memorization of the Multiplication Table as a sort of Dodge Ball contest. But we must remember, some students are slow at memorizing and others fast, so we must never embarrass any student. Always have learning and teaching on a positive upward motivation. Never ever make fun or light of a student slow to learn. And the teacher has to guard and protect the slow learners. 

So, we review multiplication tables. Now review add and subtract decimals, and multiply with decimals. But the biggest review is Long Division. And on the first day of class, tell the students then must have two papers which they will be working in class and at home, for homework for several weeks. What they are going to do is learn something about Infinity and angles at infinity and about five beautiful objects in Nature-- the five regular-polyhedra. Teacher show them the dice. But now, show them two papers where the teacher has already done the homework exercise. 

Divide the below number of 603 digits by 12, where the division is done all on one side of a paper 
 31415926535 8979323846 2643383279 5028841971 6939937510 
 5820974944 5923078164 0628620899 8628034825 3421170679   
 8214808651 3282306647 0938446095 5058223172 5359408128 
 4811174502 8410270193 8521105559 6446229489 5493038196 
 4428810975 6659334461 2847564823 3786783165 2712019091 
 4564856692 3460348610 4543266482 1339360726 0249141273   
 7245870066 0631558817 4881520920 9628292540 9171536436 
 7892590360 0113305305 4882046652 1384146951 9415116094   
 3305727036 5759591953 0921861173 8193261179 3105118548 
 0744623799 6274956735 1885752724 8912279381 8301194912 
 9833673362 4406566430 8602139494 6395224737 1907021798   
 6094370277 0539217176 2931767523 8467481846 7669405132 
 00 

Now, after the above is done, on a second paper, both front and back divide by 72 this 1208 digit number 

 31415926535 8979323846 2643383279 5028841971 6939937510 
 5820974944 5923078164 0628620899 8628034825 3421170679   
 8214808651 3282306647 0938446095 5058223172 5359408128 
 4811174502 8410270193 8521105559 6446229489 5493038196 
 4428810975 6659334461 2847564823 3786783165 2712019091 
 4564856692 3460348610 4543266482 1339360726 0249141273   
 7245870066 0631558817 4881520920 9628292540 9171536436 
 7892590360 0113305305 4882046652 1384146951 9415116094   
 3305727036 5759591953 0921861173 8193261179 3105118548 
 0744623799 6274956735 1885752724 8912279381 8301194912 
 9833673362 4406566430 8602139494 6395224737 1907021798   
 6094370277 0539217176 2931767523 8467481846 7669405132 
 0005681271 4526356082 7785771342 7577896091 7363717872 
1468440901 2249534301 4654958537 1050792279 6892589235 
4201995611 2129021960 8640344181 5981362977 4771309960   
5187072113 4999999837 2978049951 0597317328 1609631859 
5024459455 3469083026 4252230825 3344685035 2619311881 
7101000313 7838752886 5875332083 8142061717 7669147303     
5982534904 2875546873 1159562863 8823537875 9375195778   
1857780532 1712268066 1300192787 6611195909 2164201989   
3809525720 1065485863 2788659361 5338182796 8230301952 
0353018529 6899577362 2599413891 2497217752 8347913151     
5574857242 4541506959 5082953311 6861727855 8890750983 
8175463746 4939319255 0604009277 0167113900 9848824012                               
8583616 

Of course, in both divisions the student needs to use the AP Long Division method where we subtract and carry over, not bring down. You have to do the Long Division by the AP method in order to use just one sheet of paper for each division, first by 12 then by 72.

Ask the 14 year old if the number looks vaguely familiar to anyone? 

AP 


Newsgroups: sci.math
Date: Sun, 22 Apr 2018 13:43:18 -0700 (PDT)

Subject: #3-2  Chapter 3 GEOMETRY LOGIC-- set theory// Teaching True Mathematics
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sun, 22 Apr 2018 20:43:19 +0000


#3-2  GEOMETRY-LOGIC-- set theory// Teaching True Mathematics

Chapter 3-2, lessons GEOMETRY-LOGIC 

Alright, well, this topic is taught to 14 year olds. And is a topic all brand new to science, to math. Set theory is not new to science or math, but the idea that Set theory belongs in Logic is brand new. 

You see, Logic with its connectors of Equal-Not, And, Or, If-then, and its existential quantifier, its every-universal quantifier were just Algebra Logic, grammar logic, and meant that the house of Geometry was totally absent and missing in Logic. This is not good that the house of Geometry is absent in logic and needs to be revealed. 

I realized that the missing house of Logic of Geometry Logic was none other than the whole of Set theory.  Set theory never belonged as a piece of mathematics. Set theory was Geometry-Logic. 

So, this chapter is totally new to all science and mathematics and Logic. And it should reveal more beautiful ideas, than already given. 

Now I need the operators of Set theory, just like we did the operators of Algebra Logic-- the AND, the EQUAL-NOT, the OR, the IF-- Then, the existence, the for-every/all. 

I need to unpack the operators of set theory. And to define set theory. 

I need to unpack all 6 operators below and show 14 year olds that this is geometry with a SPIN motion 


ALGEBRAIC LOGIC = connectors 
1) Equal-Not (multiply) TTTT 
2) And (add) TTTF 
3) Or (subtract) FTTF 
4) If->then (divide) TFUU 
5) Existential quantifier 
6) Universal quantifier

GEOMETRY LOGIC = Set theory 
  
1) Toto Space Product (multiply) 
2) Union (add) 
3) Set Difference (subtract) 
4) Intersection (divide) 
5) Cardinality (Existence quantifier) 
6) Cartesian Product (Universal quantifier) 

The Toto Space Product I save for last, even though I list it first. The list is patterned after the Algebra Logic

Teacher-- make a review, briefly of Algebra Logic to see if the students are fresh and alert or if rusty on them. Review with examples.

2 AND 5 is what?

What is the Truth Table of AND?

3 OR 7 is what?

What is the truth table of OR?

If 9 times 6 is 54, then, 54 divided by 6 is what?
If 9 times 6 is 54, then, 54 divided by 9 is what?

What is the truth table of IF->Then? Remember

We start Geometry-Logic with Union (add) and Set Difference (subtract)

We do this with our figures of geometry on graph paper.

But first we need to define what a Set is. A set is a **geometry figure** that has graph coordinate points as its elements or members. The elements of a set are written as coordinate points (1,0) or (2,4) for example, and the set is distinguished by the symbols {(1,0) (2,4) } with its graph points inside.

Now, Set theory is a GEOMETRY FIGURE, for the figure is the container of the set, or the bag or sack that holds the elements. Set theory is confined to Mathematics as geometry. Physics and chemistry has a set theory as Atoms or magnetic monopoles being the elements. 



#3-3  GEOMETRY LOGIC-- set theory// Teaching True Mathematics

Let us review what a Set is. A set is a **geometry figure** that has graph coordinate points as its elements or members. The elements of a set are written as coordinate points (1,0) or (2,4) for example, and the set is distinguished by the symbols {(1,0) (2,4) } with its graph points inside.

Now, Set theory is a GEOMETRY FIGURE, for the figure is the container of the set, or the bag or sack that holds the elements. Set theory is confined to Mathematics as geometry. Physics and chemistry has a set theory as Atoms or magnetic monopoles being the elements. 

Triangles: Set A triangle {(7,3) (10,6) (12,3)} and Set B triangle {(7,3) (10,6) (13,4)}

Now Set A and Set B each has three elements. The number of elements we call the set Cardinality.

And in Set A we graph its three points then connect the three points with straightline segments.

So Set A is a triangle and notice it is a container a bag or sack for the three elements as points.

Set A is just the three sides of the triangle.

Now, plot the points (10,5) (11,5) and see that they are inside points of triangle {(7,3) (10,6) (12,3)}

So, set C = {(7,3) (10,6) (12,3) (10,5) (11,5)} and set C is a Geometric Figure of a triangle and its interior.

A triangle alone is its three sides, without its interior.

A triangle plus its interior, a triangle and its interior is a geometric figure.

A subset of set C is the triangle sides alone set A = {(7,3) (10,6) (12,3)}

Can we have a set in which we have just the interior of a triangle and not have its triangle sides?

The answer is no, and is a famous math problem called 4 Color Mapping, which you will learn later in this book, in College mathematics.

Square: Set S = {(2,6) (6,6) (6,10) (2,10) } and then trapezoid Set T = {(2,0) (2,6) (6,10) (6,0)}

Rectangle: Set R = {(13,4) (17,4) (17,11) (13,11)}


Parallelogram: Set P = { (19,14) (25,14) (28,17) (22,17) }

Rhombus: Set Rh = { (21,4) (26,4) (30,7) (25,7) } 

So a set is defined as the Coordinate Points of Space, those discrete points, with holes and gaps in between successor points. 
> 
> So the set A of triangle 
> 
> 
> > Triangles: Set A triangle {(7,3) (10,6) (12,3)} and Set B triangle {(7,3) (10,6) (13,4)} 
> > 
> 
> Now that triangle of set A are three members of the set, three coordinate points, so the triangle is the three sides. There are two coordinate points of (10,5) and (11,5) that are part of the interior of the triangle. 
> And if we include all numbers of the 10 Grid there would be ten more members of coordinate points from 
> (10,5) to (11,5) of  (10.1, 5) (10.2, 5) (10.3,5) etc 
> 
> So, why is this important to define Set members as being only Coordinate Points of a Graph. Why not do what Old Math did, Set as some illusive notion with a "membership test". Why not speak of the Set of all Even Integers or the set of all Odd Integers as sets, whereas here, we can only speak of all Even Integers as (2,0) (4,0) (6,0) etc (ignoring 0). 
> 
> Old Math would have {2,4,6,8,...} unioned with odd {1,3,5,7,....} equals {1,2,3,4,5,....} 
> 
> New Math would have that as {(2,0) (4,0) (6,0),....} unioned with {(1,0) (3,0), (5,0),....} equals 
> {(1,0) (2,0) (3,0) (4,0),....} 
> 
> So, what is the fuss? What is the difference? The difference is that Set theory has to be a container of some sort and so to call a set {2,4,6,8,...} as set, it has no container. It has members or elements but no container, no bag to hold the elements. 
> 

In Set theory, two ideas have to emerge in prominence-- the idea of a container-- a figure and the second idea of members or elements. 

In Old Math, to simply say Evens is {2,4,6,8,...} has no container, it has members but no container, no bag, no sack. 

In New Math, by making all elements of Sets as coordinate points, we automatically have a container because the geometric figure those points outline is the Set Container. 

On the other hand, the set as  {(2,0) (4,0) (6,0),....} has a container being a x-axis straightline segment. Same goes for the triangle above of {(7,3) (10,6) (12,3)} 

Now if the Even Numbers is a set as a line segment as the x-axis, one may question that the Odd numbers are on that same x-axis line segment and no need to form a union. But here, we must realize that a set as a container as a geometry figure is recognized as a Distinct Set by its members. 

This is where we define Set and Subset together. For a subset is the same Set Container but different amount of members. 

Now, how does this definition of Set bypass all that obnoxious phony Set of All Sets (also known as Barber Paradox). How does it bypass that fakery? Well, it bypasses or dissolves the paradox because Space of the Plane in 2nd Dimension geometry or 3rd D geometry are all inclusive, no paradox can arise. 

In fact, I prefer that we dismiss the term "set" altogether and use the term Geometric Figure. But the trouble with dismissing the word "set" is that it is too much in use in language, too much in vogue. 

Somehow languages love to have several words that mean almost the same thing, with shades or nuances of tiny differences. A poor language is one in which "one size fits all" in meaning. A language is better when we have the words "use" and "vogue" meaning almost the same things but slightly different. 

Set theory means the same thing as Geometric Figures. In that sense, set theory is a part of mathematics and is not physics, nor chemistry nor biology. However, if physics uses Elements of atoms or magnetic monopoles, then physics can call a set of all matter in a given space. Or chemistry can call a set of all atoms in a given space. Or biology can call the set of all oak trees because of the element of DNA as DNA is geometrical in the mapping of Plantae, Angiosperms, Eudicots, Rosids, Fagales, Fagaceae, Quercus 

AP 

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#413171 — 3-4 Chapter 3 for age 14// Teaching True Mathematics

#3-4  Union & Set Difference in Geometry Logic// Teaching True Mathematics

GEOMETRY LOGIC = Set theory 
  
1) Toto Space Product (multiply) 
2) Union (add) 
3) Set Difference (subtract) 
4) Intersection (divide) 
5) Cardinality (Existence quantifier) 
6) Cartesian Product (Universal quantifier) 

Now of the six operators above, it is easy for the students to recognize that union is add and set-difference is subtract. Very easy to see that Union is like AND in Algebra Logic, where it puts things together, it adds things together.


So let us do some Union exercises. We have square sets to plot
A = {(0,0) (1,0) (1,1) (0,1) }
B = {(1,0) (3,0) (3,2) (1,2) }
C = {(3,0) (6,0) (6,3) (3,3) }
So plot those three squares and connect the points by straightline segments.

We designate union by U so what is the union of A,B, 

AUB = {(0,0) (1,0) (1,1) (0,1) (1,0) (3,0) (3,2) (1,2) } now we remove all duplicates

AUB =  {(0,0) (1,0) (1,1) (0,1) (3,0) (3,2) (1,2) }

So, now student what is AUC, then do BUC

Set-difference is subtraction, and is much like in Algebra Logic a picking of one thing and a discard of the other, as is OR in Algebra Logic. The discard being the subtraction.

A = {(0,0) (1,0) (1,1) (0,1) }
B = {(1,0) (3,0) (3,2) (1,2) }
C = {(3,0) (6,0) (6,3) (3,3) }
D = {(0,0)}
E = {(1,1)}
F = {(1,0)}
G = {(3,2)}
H = {(3,0)}
I  = {(6,3)}
J = {(0,1) (1,0)}
K = {(1,0) (3,2)}
L = {(3,3) (6,0)}

We write Set Difference just as we write subtraction, so set A subtract D is 
A - D = {(0,0) (1,0) (1,1) (0,1) } - {(0,0)} = { (1,0) (1,1) (0,1) } Now plot and connect with straightline segments and see it is a right-triangle. It started as set A a square and with subtraction of a point is now a right triangle

A - J = {(0,0) (1,0) (1,1) (0,1) } - {(0,1) (1,0)} = { (0,0) (1,1) } Now plot and connect with straightline segment and see it is a straightline segment itself. It started as set A a square and ended up being a straightline segment.

As exercises do these:
A - E 
B - F
B - G
B - K
C - H
C - I
C - L
Plot them and connect with straightline segments the Set Difference and then tell what the end figure is.

AP 

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#413173 — 3-5 Chapter 3 for age 14// Teaching True Mathematics

#3-5  Intersection in Geometry Logic// Teaching True Mathematics

GEOMETRY LOGIC = Set theory 
  
1) Toto Space Product (multiply) 
2) Union (add) 
3) Set Difference (subtract) 
4) Intersection (divide) 
5) Cardinality (Existence quantifier) 
6) Cartesian Product (Universal quantifier) 

Now, some may find it hard to believe that intersection of two objects is division. But think of the word "intersection" itself, for intersection means to cut. Now in Algebra Logic, division was IF-> Then, and it is probably more difficult to see how If->then is division than seeing how intersection is division. Review If --> Then with its truth table of TFUU. Such examples as-- If it rains, then the Sun is not out. We sort of see that more as a "consequence" that if it rains then the consequence is the Sun is not out. But, we can see it as division, that If it rains then the Sun is not out, so we divided the prospects of the day into two realms-- a realm of raining and a realm of Sun being out.

Now in Old Logic the symbol for Intersect was the upside down U, but since my keyboard does not have a upside down U , I will use "intersect".

Now plot these Sets given

a = {(0,0) (6,6) }
b = {(2,6) (7,3) }
c = {(13,11) (17,11) }
d = {(14,10) (16,12) }
e = {(10,6) (12,3) }
f  = {(7,3) (13,4) }

For example the a intersect b = {(0,0) (6,6) } intersect {(2,6) (7,3) } here you have to connect the two points in each set with a straightline segment. So get out the ruler and connect and then find the intersection point. I get a (4.5, 4.5) with my eyeball, but there is probably some sigma error here. Some people may get (4.6, 4.6)

Have the students try their hand at doing 

c intersect d
e intersect f

And teacher make your own intersect problems, such as the intersection of square and rectangle
g = {(0,0) (1,0) (1,1) (0,1) }
h = {(1,1) (0,1) (0,4) (1,4) }
i  = {(1,0) (1,1) (5,0) (5,1) }

What is g intersect h
What is g intersect i
An interesting example is what is h intersect i, and since there are no points in common, we say this set is 0, as in zero of numbers. Old Math and Old Logic called this intersection the empty set, but we know better, because a set is defined as a figure with points. So to say "empty set" is a contradiction in logic itself. Whenever we have "nothing" we have 0. 

AP

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#413175 — Experimenting with ellipse & oval tubes Teaching True Mathematics

Ellipse tube sections seem to generate more ellipses

Oval tube sections have the potential of generating all three possibilities— oval, circle, ellipse

Sort of reminds me — square is a rectangle is a parallelogram

AP

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#413181 — Re: Experimenting with ellipse & oval tubes Teaching True Mathematics

On 2018-05-16 08:46:54 +0000, Archimedes Plutonium said:

> Ellipse tube sections seem to generate more ellipses
> 
> Oval tube sections have the potential of generating all three 
> possibilities— oval, circle, ellipse
> 
> Sort of reminds me — square is a rectangle is a parallelogram
> 
> AP

*
AP:

Please show us the equation for an oval.

Thanks,

earle
*

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#413184 — Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics

On Wednesday, May 16, 2018 at 3:47:03 AM UTC-5, Archimedes Plutonium wrote:
> Ellipse tube sections seem to generate more ellipses
> 
> Oval tube sections have the potential of generating all three possibilities— oval, circle, ellipse
> 
> Sort of reminds me — square is a rectangle is a parallelogram
> 

Now one can type in ellipse tube into google search and easily get pictures, but the trouble with Old Math, is the ignorant bards could never separate out-- oval is not a ellipse, could never refine that Oval has just one axis of symmetry. Through the centuries and milleniums of math history, everyone was brain-dead over the topic of oval versus ellipse. As if the muses came to earth and placed a huge shroud of fog into the minds of all those that ever came upon the topic of oval and ellipse, and made them nattering nutter dumb on the topic.

So if you type in oval tube, you only get ellipse tubes. A ellipse tube has two axes of symmetry. A oval tube has just one axis of symmetry.

Now, I have the conjecture that sectioning or cutting these three types of tubes yields these three different results.


type of tube         possible results from cuttings

cone tube                circle, oval

cylinder tube            circle, ellipse

ellipse tube               ellipses only  ??

oval tube                  oval, ellipse, circle ??

Now I placed a question mark over the ones I am not sure of. So let that be a conjecture, that only the oval tube can afford the possible creation of all three figures, and the ellipse tube can only afford more ellipses.

Now to help me unravel this mystery, I am trying to construct a dual similar geometry of straightline figures only such as square, rectangle , parallelogram with their 3D counterparts. Mind you, I am only doing this to gain insight into the above.

type of tube                        possible results from cuttings

cube                                            square, rectangle

rectangular solid tube                rectangles only

parallelogram tube                       parallelograms only ??

parallelepiped tube                       parallelograms only ??

Seems to me there should be some 3D figure when cut, yields all three -- square, rectangle, parallelogram
But maybe that is impossible and thus the oval tube cut is not yielding circle, ellipse, oval

AP

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#413265 — better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics

Alright, some really good progress on this front.

On Wednesday, May 16, 2018 at 1:05:46 PM UTC-5, Archimedes Plutonium wrote:
> On Wednesday, May 16, 2018 at 3:47:03 AM UTC-5, Archimedes Plutonium wrote:
> > Ellipse tube sections seem to generate more ellipses
> > 
> > Oval tube sections have the potential of generating all three possibilities— oval, circle, ellipse
> > 
> > Sort of reminds me — square is a rectangle is a parallelogram
> > 
> 
> Now one can type in ellipse tube into google search and easily get pictures, but the trouble with Old Math, is the ignorant bards could never separate out-- oval is not a ellipse, could never refine that Oval has just one axis of symmetry. Through the centuries and milleniums of math history, everyone was brain-dead over the topic of oval versus ellipse. As if the muses came to earth and placed a huge shroud of fog into the minds of all those that ever came upon the topic of oval and ellipse, and made them nattering nutter dumb on the topic.
> 
> So if you type in oval tube, you only get ellipse tubes. A ellipse tube has two axes of symmetry. A oval tube has just one axis of symmetry.
> 
> Now, I have the conjecture that sectioning or cutting these three types of tubes yields these three different results.
> 
> 
> type of tube         possible results from cuttings
> 
> cone tube                circle, oval
> 
> cylinder tube            circle, ellipse
> 
> ellipse tube               ellipses only  ??
> 
> oval tube                  oval, ellipse, circle ??
> 
> Now I placed a question mark over the ones I am not sure of. So let that be a conjecture, that only the oval tube can afford the possible creation of all three figures, and the ellipse tube can only afford more ellipses.
> 
> Now to help me unravel this mystery, I am trying to construct a dual similar geometry of straightline figures only such as square, rectangle , parallelogram with their 3D counterparts. Mind you, I am only doing this to gain insight into the above.
> 
> type of tube                        possible results from cuttings
> 
> cube                                            square, rectangle
> 
> rectangular solid tube                rectangles only
> 

Here is much ambiguity for the above is only for a rectangle solid in which all three parameters x,y,z are different, but we know a rectangle solid like 3 by  2 by 2 can yield a square.

So this needs tinkering




> parallelogram tube                       parallelograms only ??
> 
> parallelepiped tube                       parallelograms only ??
> 
> Seems to me there should be some 3D figure when cut, yields all three -- square, rectangle, parallelogram
> But maybe that is impossible and thus the oval tube cut is not yielding circle, ellipse, oval
> 
> 

Alright, what I need is something with a "pointed head" like a cone to a cylinder. And for straightline only figures. And that is a square pyramid

type of tube                        possible results from cuttings

cube                                            square, rectangle

square pyramid                           square, trapezoid, triangle

triangle solid                              triangles only??

trapezoid solid                            trapezoids only??

There, that's better.

AP

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#413267 — Re: better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics

On Thursday, May 17, 2018 at 12:53:12 PM UTC-5, Archimedes Plutonium wrote:
> Alright, some really good progress on this front.
> 
> On Wednesday, May 16, 2018 at 1:05:46 PM UTC-5, Archimedes Plutonium wrote:
> > On Wednesday, May 16, 2018 at 3:47:03 AM UTC-5, Archimedes Plutonium wrote:
> > > Ellipse tube sections seem to generate more ellipses
> > > 
> > > Oval tube sections have the potential of generating all three possibilities— oval, circle, ellipse
> > > 
> > > Sort of reminds me — square is a rectangle is a parallelogram
> > > 
> > 
> > Now one can type in ellipse tube into google search and easily get pictures, but the trouble with Old Math, is the ignorant bards could never separate out-- oval is not a ellipse, could never refine that Oval has just one axis of symmetry. Through the centuries and milleniums of math history, everyone was brain-dead over the topic of oval versus ellipse. As if the muses came to earth and placed a huge shroud of fog into the minds of all those that ever came upon the topic of oval and ellipse, and made them nattering nutter dumb on the topic.
> > 
> > So if you type in oval tube, you only get ellipse tubes. A ellipse tube has two axes of symmetry. A oval tube has just one axis of symmetry.
> > 
> > Now, I have the conjecture that sectioning or cutting these three types of tubes yields these three different results.
> > 
> > 
> > type of tube         possible results from cuttings
> > 
> > cone tube                circle, oval
> > 
> > cylinder tube            circle, ellipse
> > 
> > ellipse tube               ellipses only  ??
> > 
> > oval tube                  oval, ellipse, circle ??
> > 
> > Now I placed a question mark over the ones I am not sure of. So let that be a conjecture, that only the oval tube can afford the possible creation of all three figures, and the ellipse tube can only afford more ellipses.
> > 
> > Now to help me unravel this mystery, I am trying to construct a dual similar geometry of straightline figures only such as square, rectangle , parallelogram with their 3D counterparts. Mind you, I am only doing this to gain insight into the above.
> > 
> > type of tube                        possible results from cuttings
> > 
> > cube                                            square, rectangle
> > 
> > rectangular solid tube                rectangles only
> > 
> 
> Here is much ambiguity for the above is only for a rectangle solid in which all three parameters x,y,z are different, but we know a rectangle solid like 3 by  2 by 2 can yield a square.
> 
> So this needs tinkering
> 
> 
> 
> 
> > parallelogram tube                       parallelograms only ??
> > 
> > parallelepiped tube                       parallelograms only ??
> > 
> > Seems to me there should be some 3D figure when cut, yields all three -- square, rectangle, parallelogram
> > But maybe that is impossible and thus the oval tube cut is not yielding circle, ellipse, oval
> > 
> > 
> 
> Alright, what I need is something with a "pointed head" like a cone to a cylinder. And for straightline only figures. And that is a square pyramid
> 
> type of tube                        possible results from cuttings
> 
> cube                                            square, rectangle
> 
> square pyramid                           square, trapezoid, triangle
> 
> triangle solid                              triangles only??

Alright, I have a tetrahedron dice sitting in front of me, and can visualize its cuts. I do see a trapezoid emerging as one of possible cuts. Not sure of one of those cuts could ever be a rectangle, I doubt it, but working things out in the head only is often erroneous. Need to actually make hands on cuts of a tetrahedron to see if a rectangle or square can emerge.


> 
> trapezoid solid                            trapezoids only??
> 
> There, that's better.
> 
> AP

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#413285 — These ideas belong in my other quest to unify Conic sections with Regular Polyhedra Re: Experimenting with ellipse & oval tubes Teaching True Mathematics

Now these ideas expressed below are part of my quest to unify the Conic Sections with the Regular Polyhedra, but in a funny manner, I need to extend the Conic Sections to include Cylinder sections. I already added the square pyramid to the Regular Polyhedra, so the extension is not too out of place.

On Thursday, May 17, 2018 at 1:10:17 PM UTC-5, Archimedes Plutonium wrote:
> On Thursday, May 17, 2018 at 12:53:12 PM UTC-5, Archimedes Plutonium wrote:
> > Alright, some really good progress on this front.
> > 
> > On Wednesday, May 16, 2018 at 1:05:46 PM UTC-5, Archimedes Plutonium wrote:
> > > On Wednesday, May 16, 2018 at 3:47:03 AM UTC-5, Archimedes Plutonium wrote:
> > > > Ellipse tube sections seem to generate more ellipses
> > > > 
> > > > Oval tube sections have the potential of generating all three possibilities— oval, circle, ellipse
> > > > 
> > > > Sort of reminds me — square is a rectangle is a parallelogram
> > > > 
> > > 
> > > Now one can type in ellipse tube into google search and easily get pictures, but the trouble with Old Math, is the ignorant bards could never separate out-- oval is not a ellipse, could never refine that Oval has just one axis of symmetry. Through the centuries and milleniums of math history, everyone was brain-dead over the topic of oval versus ellipse. As if the muses came to earth and placed a huge shroud of fog into the minds of all those that ever came upon the topic of oval and ellipse, and made them nattering nutter dumb on the topic.
> > > 
> > > So if you type in oval tube, you only get ellipse tubes. A ellipse tube has two axes of symmetry. A oval tube has just one axis of symmetry.
> > > 
> > > Now, I have the conjecture that sectioning or cutting these three types of tubes yields these three different results.
> > > 
> > > 
> > > type of tube         possible results from cuttings
> > > 
> > > cone tube                circle, oval
> > > 
> > > cylinder tube            circle, ellipse
> > > 
> > > ellipse tube               ellipses only  ??
> > > 
> > > oval tube                  oval, ellipse, circle ??
> > > 

Trouble here is that for 3,000 years now, mathematics was under a delusion spell, a total mind blackout that ellipse is never a conic but rather-- the oval is. And being under that mind-black-out, no-one could even see that there were other geometry figures to examine and research.

> > > Now I placed a question mark over the ones I am not sure of. So let that be a conjecture, that only the oval tube can afford the possible creation of all three figures, and the ellipse tube can only afford more ellipses.
> > > 
> > > Now to help me unravel this mystery, I am trying to construct a dual similar geometry of straightline figures only such as square, rectangle , parallelogram with their 3D counterparts. Mind you, I am only doing this to gain insight into the above.
> > > 
> > > type of tube                        possible results from cuttings
> > > 
> > > cube                                            square, rectangle
> > > 
> > > rectangular solid tube                rectangles only
> > > 

Here I needed a pointed head figure like the cone is pointed head versus the cylinder.

> > 
> > Here is much ambiguity for the above is only for a rectangle solid in which all three parameters x,y,z are different, but we know a rectangle solid like 3 by  2 by 2 can yield a square.
> > 
> > So this needs tinkering
> > 
> > 
> > 
> > 
> > > parallelogram tube                       parallelograms only ??
> > > 
> > > parallelepiped tube                       parallelograms only ??
> > > 

Again, here I needed a pointed head figure and the square pyramid is just the thing.



> > > Seems to me there should be some 3D figure when cut, yields all three -- square, rectangle, parallelogram
> > > But maybe that is impossible and thus the oval tube cut is not yielding circle, ellipse, oval
> > > 
> > > 
> > 
> > Alright, what I need is something with a "pointed head" like a cone to a cylinder. And for straightline only figures. And that is a square pyramid
> > 
> > type of tube                        possible results from cuttings
> > 
> > cube                                            square, rectangle
> > 
> > square pyramid                           square, trapezoid, triangle
> > 
> > triangle solid                              triangles only??
> 
> Alright, I have a tetrahedron dice sitting in front of me, and can visualize its cuts. I do see a trapezoid emerging as one of possible cuts. Not sure of one of those cuts could ever be a rectangle, I doubt it, but working things out in the head only is often erroneous. Need to actually make hands on cuts of a tetrahedron to see if a rectangle or square can emerge.
> 

Please do not hold me to this, but I believe I can get a square and a rectangle out of a tetrahedron cut.



> 
> > 
> > trapezoid solid                            trapezoids only??
> > 
> > There, that's better.
> > 

I think the trapezoid solid sections would be like the Oval Tube sections in that they -- both of them can give rise to all the other figures of that category class.

AP

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#413292 — Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test

Village Idiot Archimedes "Failure" Plutonium <plutonium.archimedes@gmail.com> babbles:

>Now these ideas expressed below are part of my quest to unify the Conic 
>Sections with the Regular Polyhedra, but in a funny manner, I need to 

Thank you for requesting another Babble-o-meter Calculation!

(still a work in progress)

☑ Archie reposts the same old, same old, yet again...
☑ ...snd again and again...
☑ ...snd again and again...
☑ ...posted enough times to be classified as spam...
☐ ...Post has no new content, in fact...
☐ ...Archie's spam complains about other spammers or babblers...
☑ ...One word: Logorrhea...
☑ ...Purpose of post is to remain #1 Front Page Hog...
☐ .....meanwhile, Archie complains of some other "Front Page Hog"...
☐ ...Post posted in the wrong topic...
☐ .....and to the wrong newsgroup...
☐ ...Author awards self Nobel Prize/claims he should be so awarded...
☐ .....Author refuses self-awarded Nobel, real awardees don't deserve it...
☐ ...Author sour grapes Nobel or other science/math prize...
☑ ...Conspiracy theories of math/science establishment suppression...
☑ ...Post has science or math 100% made up from whole cloth...
☑ ...Post's science/math based on earlier whole cloth science/math...
☑ .....which was based on even earlier whole cloth science/math...
☑ .....which was, oh never mind...
☑ ...Post contains The Truth because Archie said it is true...
☑ ...Phrases such as "Old Science" (actual science) and "New Science (babbling of author)...
☑ ...Another word: Graphomania...
☐ ...Author thinks cutting up magazines disproves actual math proofs...
☑ ...Author thinks a bad dream is an excellent basis for physics...
☑ ...Archie doesn't understand Usenet, even after 26+ years...
☐ ...Archie asks Google Groups to do something they can't do... 
☑ ...Archie even thinks Google runs Usenet...
☑ .....even though Archie used Usenet even before there even was a Google...
☑ ...Archie won't engage in discussion in a discussion group...
☐ ...Writes "Keep out of my threads!"...
☐ ...Archie demands professors resign for not teaching his broken math...
☐ ...Archie outwitted by someone too stoopid to come out of the rain AGAIN...
☑ ...and Archie can't get over the shame of messing up percentages...
☑ ....he even still thinks 8.88 is "exactly" 9...
☐ ....and he thinks 16.81 is "spot on" 17...
☐ ...Archie is envious that I weighed the electron and he didn't...
☐ ...Post includes the dumb ascii art cat/owl thing...
☑ ...Post contains ascii art of Archie's butthole...
☑ ...and Archie doesn't realize ascii art is so 1980s...
☑ ...Archie tries to involve totally uninvolved people...
☐ .....with a subject about flunking a nonexistent test no one ever took...
☐ .....but has no clue they will never see his post...
☐ .....and has no clue they probably don't know what Usenet is...
☐ .....he expects them to have power/authority they simply don't...
☐ ...Post includes a stalker list of physics and/or math professors...
☑ ...Too stoopid to realize attack posts just produce more posts like this...
☑ ...Google Groups poster. 'Nuf said.

Archie's Babbling Nonsense score:  26 plutoniums!

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#413272 — Re: Archimedes "Failure" Plutonium flunks the lifelong Math test

Archimedes "Failure" Plutonium <plutonium.archimedes@gmail.com> writes:

>Michael Moroney 	writes:
>1:21 AM (10 hours ago)

>> "Failure"

No, Archimedes "Failure" Plutonium, that's 'Archimedes "Failure" Plutonium'.

>Gary Feldman,Marty Walsh, Charlie Baker, Douglas Finkbeiner, Melissa Frankl=in,

Let's score this fine example of Plutonium failing!

☑ Archie responds to criticism but is unable to discuss the issue...
☑ ...Zero new content, in fact...
☑ ...Giggle Groups screenshot cut and pasted...
☑ ...with Archie's response posted in the wrong topic...
☐ ...and to the wrong newsgroup...
☑ ...multiple times...
☑ ...enough times to be classified as spam...
☑ ...in a topic/topics explicitly created by him for doing so...
☐ ...and Archie even whines about (other) spammers in his spam...
☐ ...with a subject about flunking a nonexistent test no one ever took...
☑ ...and the subject mentions totally uninvolved people...
☑* ...who are university math or physics professors...
☑ ...at a university supposedly near the person criticizing Archie...
☐ ...but Archie got the location (and university) completely wrong...
☐ ...and Archie demands they resign for not teaching his broken math...
☑ ...and he includes a stalker list of physics and/or math professors...
☑ ...and STILL can't answer 'why stalker lists of uninvolved profs'...
☑ ...and Archie's actual response is completely unrelated to the topic...
☑ ...and the critic's comment has embarrassing (to AP) portion removed...
☑ ...to the extent the comment is no longer recognizable...
☐ ...includes random snippets by other critics, spammers or babblers...
☐ ...which are attributed to yet other critics, spammers or babblers...
☑ ...followed by yet another repost of the "12 Failures of Plutonium"...
☑ ...or the "you gotta draw pictures of calculus" repost...
☑ ...and includes the dumb ascii art cat/owl thing...
☐ ...as well as ascii art of Archie's butthole...
☑ ...and Archie doesn't realize ascii art is so 1980s...
☑ ...and Archie brings up a "mistake" (in his view) from months ago...
☑ ...which, of course, is not actually a mistake...
☑ ...and Archie invents yet more "mistakes" (that are not mistakes)...
☐ ...and Archie really wears out the "a beer short of a 6 pack" joke...
☐ ...but he still doesn't realize he's about 5 beers short...
☑ ...and Archie can't get over the shame of messing up percentages...
☑ ...and Archie is envious that I weighed the electron and he didn't...
☑ ...he even still thinks 8.88 is "exactly" 9...
☐ ...and he thinks 16.81 is "spot on" 17...
☐ ...Archie asks Google Groups to do something they can't do... 
☑ ...One word. Logorrhea.  ...
☑ ...Google Groups poster. 'Nuf said. 

Archimedes Plutonium Failure score:  27 plutoniums of failure!!

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#413198 — 3-5 Chapter 3 for age 14// Teaching True Mathematics

Funny how Cartesian Product is not really a product at all but is the universal quantifier and the wellhead source for what gives rise to the “function concept”.

AP

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#413291 — Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

On Wednesday, May 16, 2018 at 2:43:36 PM UTC-5, Archimedes Plutonium wrote:
> Funny how Cartesian Product is not really a product at all but is the universal quantifier and the wellhead source for what gives rise to the “function concept”.
> 
> 

So you have to wonder how the term Product got into Cartesian Product. Was it because like in our example of x axis having six numbers, 0,1,2,3,4,5 and y axis having the same six numbers, that 6 x 6 = 36 covers all these arrangements?

(0,0) (0,1), (0,2), (0,3),,, out to (5,4) (5,5)  all 36 of them

However, trouble is, if we insist on being more general, say the x axis was 1,2,3 and y axis is 4,5

then we would think there are 3 x 2 = 6 arrangements of Cartesian Product

(1,4) (1,5) (2,4) (2,5) (3,4) (3,5) but we then lose out on the reverse, what in function theory would be the inverse function of mapping from the y axis into the x-axis

(4,1) (5,1) (4,2) (5,2) (4,3) (5,3)

So the name Cartesian Product was a poor choice of term "product"

What I think the name should have been was Cartesian Universal Function. And thus we introduce the concept of function from set theory of Geometric Logic.

AP

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#413294 — Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test

Village Idiot Archimedes "Failure" Plutonium <plutonium....@gmail.com> babbles:

<snip babble>

Thank you for requesting another Babble-o-meter Calculation!

(still a work in progress)

☑ Archie reposts the same old, same old, yet again...
☑ ...snd again and again...
☑ ...snd again and again...
☑ ...posted enough times to be classified as spam...
☑ ...Post has no new content, in fact...
☐ ...Archie's spam complains about other spammers or babblers...
☑ ...One word: Logorrhea...
☑ ...Purpose of post is to remain #1 Front Page Hog...
☐ .....meanwhile, Archie complains of some other "Front Page Hog"...
☐ ...Post posted in the wrong topic...
☐ .....and to the wrong newsgroup...
☐ ...Author awards self Nobel Prize/claims he should be so awarded...
☐ .....Author refuses self-awarded Nobel, real awardees don't deserve it...
☐ ...Author sour grapes Nobel or other science/math prize...
☑ ...Post has science or math 100% made up from whole cloth...
☑ ...Post's science/math based on earlier whole cloth science/math...
☑ .....which was based on even earlier whole cloth science/math...
☑ .....which was, oh never mind...
☑ ...Post contains The Truth because Archie said it is true...
☑ ...Phrases such as "Old Science" (actual science) and "New Science (babbling of author)...
☑ ...Another word: Graphomania...
☐ ...Author thinks cutting up magazines disproves actual math proofs...
☑ ...Author thinks a bad dream is an excellent basis for physics...
☑ ...Archie doesn't understand Usenet, even after 26+ years...
☐ ...Archie asks Google Groups to do something they can't do... 
☑ ...Archie even thinks Google runs Usenet...
☑ .....even though Archie used Usenet even before there even was a Google...
☑ ...Archie won't engage in discussion in a discussion group...
☐ ...Writes "Keep out of my threads!"...
☐ ...Archie demands professors resign for not teaching his broken math...
☐ ...Archie outwitted by someone too stoopid to come out of the rain AGAIN...
☑ ...and Archie can't get over the shame of messing up percentages...
☑ ....he even still thinks 8.88 is "exactly" 9...
☐ ....and he thinks 16.81 is "spot on" 17...
☐ ...Archie is envious that I weighed the electron and he didn't...
☐ ...Post includes the dumb ascii art cat/owl thing...
☑ ...Post contains ascii art of Archie's butthole...
☑ ...and Archie doesn't realize ascii art is so 1980s...
☑ ...Archie tries to involve totally uninvolved people...
☐ .....with a subject about flunking a nonexistent test no one ever took...
☐ .....but has no clue they will never see his post...
☐ .....and has no clue they probably don't know what Usenet is...
☐ .....he expects them to have power/authority they simply don't...
☐ ...Post includes a stalker list of physics and/or math professors...
☑ ...Too stoopid to realize attack posts just produce more posts like this...
☑ ...Google Groups poster. 'Nuf said.

Archie's Babbling Nonsense score:  26 plutoniums!

[toc] | [prev] | [next] | [standalone]

#413297 — Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

#3-8  Toto Space Product in Geometry Logic// Teaching True Mathematics

GEOMETRY LOGIC = Set theory 
  
1) Toto Space Product (multiply) 
2) Union (add) 
3) Set Difference (subtract) 
4) Intersection (divide) 
5) Cardinality (Existence quantifier) 
6) Cartesian Product (Universal quantifier) 

Of the six operators above, this Toto Space is perhaps the most important because it is the entire geometry in which these six operators work in, and on top of that, it is this operator that provides motion in geometry to form geometry figures. The motion is a "spin".

So, we have a lot of work to do on this last but important operator.

Now the Toto Space Product is truly a product, and for 10 Grid would be this--- first we list all of 10 Grid

0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, ... , 9.8, 9.9, 10.0

Here we did it for 8 year olds in chapter 1, lesson 1-1

9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 

If we do not count 0.0 then there are 10 x 10 = 100 numbers there in the 10 Grid. But, the Toto Space Product of 10 Grid is 10^2 = 100 and all of the numbers in 100 Grid.

100 Grid numbers are these

0.00, .01, .02, .03, .... , 99.98, 99.99, 100.00

Not counting 0.00, how many numbers are there in 100 Grid? Well, there are 100 integers and there are 100 decimal fractions between any two consecutive or successor integers. That means, say, between 1 and 2 there are 100 decimal fractions, between 2 and 3 there are 100 decimal fractions. So between 0 and 100 there are 100 integers and between any two consecutive integers there are 100 decimal fractions, hence, 100 x 100 = 10,000.

So, the Toto Space of 10 Grid is 10,000 numbers.

The Toto Space of 10 Grid is 10,000 numbers yet we only see 100 of those numbers on the x-axis. So where did the 10,000 - 100 = 9,900 other numbers go? 

So in 10 Grid we have 100 points on a graph for x-axis. Yet the Toto Space of 10 Grid is 10,000 points on x-axis. Those other 9,900 points such as 10.01, 10.02, 10.03, . . . 99.98, 99.99, 100.00 are curling back around to 0 in a circle.

More later,....

AP

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#413299 — Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test

Village Idiot Archimedes "Failure" Plutonium <plutonium.archimedes@gmail.com> babbles:



>#3-8  Toto Space Product in Geometry Logic// Teaching True Mathematics

>GEOMETRY LOGIC = Set theory 

Thank you for requesting another Babble-o-meter Calculation!

(still a work in progress)

☑ Archie reposts the same old, same old, yet again...
☑ ...snd again and again...
☑ ...snd again and again...
☑ ...posted enough times to be classified as spam...
☐ ...Post has no new content, in fact...
☐ ...Archie's spam complains about other spammers or babblers...
☑ ...One word: Logorrhea...
☑ ...Purpose of post is to remain #1 Front Page Hog...
☐ .....meanwhile, Archie complains of some other "Front Page Hog"...
☐ ...Post posted in the wrong topic...
☐ .....and to the wrong newsgroup...
☐ ...Author awards self Nobel Prize/claims he should be so awarded...
☐ .....Author refuses self-awarded Nobel, real awardees don't deserve it...
☐ ...Author sour grapes Nobel or other science/math prize...
☑ ...Post has science or math 100% made up from whole cloth...
☑ ...Post's science/math based on earlier whole cloth science/math...
☑ .....which was based on even earlier whole cloth science/math...
☑ .....which was, oh never mind...
☑ ...Post contains The Truth because Archie said it is true...
☐ ...Phrases such as "Old Science" (actual science) and "New Science (babbling of author)...
☑ ...Another word: Graphomania...
☐ ...Author thinks cutting up magazines disproves actual math proofs...
☑ ...Author thinks a bad dream is an excellent basis for physics...
☑ ...Archie doesn't understand Usenet, even after 26+ years...
☐ ...Archie asks Google Groups to do something they can't do... 
☑ ...Archie even thinks Google runs Usenet...
☑ .....even though Archie used Usenet even before there even was a Google...
☑ ...Archie won't engage in discussion in a discussion group...
☐ ...Writes "Keep out of my threads!"...
☐ ...Archie demands professors resign for not teaching his broken math...
☐ ...Archie outwitted by someone too stoopid to come out of the rain AGAIN...
☑ ...and Archie can't get over the shame of messing up percentages...
☑ ....he even still thinks 8.88 is "exactly" 9...
☐ ....and he thinks 16.81 is "spot on" 17...
☐ ...Archie is envious that I weighed the electron and he didn't...
☐ ...Post includes the dumb ascii art cat/owl thing...
☐ ...Post contains ascii art of Archie's butthole...
☐ ...and Archie doesn't realize ascii art is so 1980s...
☐ ...Archie tries to involve totally uninvolved people...
☐ .....with a subject about flunking a nonexistent test no one ever took...
☐ .....but has no clue they will never see his post...
☐ .....and has no clue they probably don't know what Usenet is...
☐ .....he expects them to have power/authority they simply don't...
☐ ...Post includes a stalker list of physics and/or math professors...
☑ ...Too stoopid to realize attack posts just produce more posts like this...
☑ ...Google Groups poster. 'Nuf said.

Archie's Babbling Nonsense score:  21 plutoniums!

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#413320 — Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

On Thursday, May 17, 2018 at 11:45:04 PM UTC-5, Archimedes Plutonium wrote:
> #3-8  Toto Space Product in Geometry Logic// Teaching True Mathematics
> 
> GEOMETRY LOGIC = Set theory 
>   
> 1) Toto Space Product (multiply) 
> 2) Union (add) 
> 3) Set Difference (subtract) 
> 4) Intersection (divide) 
> 5) Cardinality (Existence quantifier) 
> 6) Cartesian Product (Universal quantifier) 
> 
> Of the six operators above, this Toto Space is perhaps the most important because it is the entire geometry in which these six operators work in, and on top of that, it is this operator that provides motion in geometry to form geometry figures. The motion is a "spin".
> 
> So, we have a lot of work to do on this last but important operator.
> 
> Now the Toto Space Product is truly a product, and for 10 Grid would be this--- first we list all of 10 Grid
> 
> 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, ... , 9.8, 9.9, 10.0
> 
> Here we did it for 8 year olds in chapter 1, lesson 1-1
> 
> 9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
> 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
> 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
> 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
> 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
> 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
> 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
> 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
> 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
> 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 
> 
> If we do not count 0.0 then there are 10 x 10 = 100 numbers there in the 10 Grid. But, the Toto Space Product of 10 Grid is 10^2 = 100 and all of the numbers in 100 Grid.
> 
> 100 Grid numbers are these
> 
> 0.00, .01, .02, .03, .... , 99.98, 99.99, 100.00
> 
> Not counting 0.00, how many numbers are there in 100 Grid? Well, there are 100 integers and there are 100 decimal fractions between any two consecutive or successor integers. That means, say, between 1 and 2 there are 100 decimal fractions, between 2 and 3 there are 100 decimal fractions. So between 0 and 100 there are 100 integers and between any two consecutive integers there are 100 decimal fractions, hence, 100 x 100 = 10,000.
> 
> So, the Toto Space of 10 Grid is 10,000 numbers.
> 
> The Toto Space of 10 Grid is 10,000 numbers yet we only see 100 of those numbers on the x-axis. So where did the 10,000 - 100 = 9,900 other numbers go? 
> 
> So in 10 Grid we have 100 points on a graph for x-axis. Yet the Toto Space of 10 Grid is 10,000 points on x-axis. Those other 9,900 points such as 10.01, 10.02, 10.03, . . . 99.98, 99.99, 100.00 are curling back around to 0 in a circle.
> 
> More later,....
> 
> AP

Re: let's do hydrogen Re: CO2 has two isomers, and plants only can use animal CO2

- show quoted text -
Happy to annouce, that since Google does not engineer a fair level playing field of its Newsgroups, by giving original authors the ability to delete not only their post, but any stalker posts within their own thread-- make original authors, the owners of their thread and the power to delete stalker posts. Happy to announce I will Reverse Engineer what Google should engineer. Thus, all my posts from now on, until Google does the right thing in engineering the delete key to original authors. All my posts will be reincarnated and other deleted as stalking poopers attempt to bully force AP out. 

An unfair system of discourse deserves unfair habits. Not a level playing field-- a field stacked in favor of persistent bullies whose only goal is to remove a poster and not do math nor physics. 

This saves me distraction and anger, but it does lose me time. It is worth it for all future posters of science and math and physics. That, as they run into hatemongering stalkers, that they have a choice of actions, other than be forced to leave. 

So, from now on, all my science, math, physics posts are posted and if a stalker invades, those are resurrected anew and the other one deleted. 

So, let's do it. 

AP

[toc] | [prev] | [next] | [standalone]

#413400 — Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

On May 18 2018, Archimedes Plutonium wrote:
> On Thursday, May 17, 2018 at 11:45:04 PM UTC-5, Archimedes Plutonium wrote:
> > #3-8  Toto Space Product in Geometry Logic// Teaching True Mathematics
> > 
> > GEOMETRY LOGIC = Set theory 
> >   
> > 1) Toto Space Product (multiply) 
> > 2) Union (add) 
> > 3) Set Difference (subtract) 
> > 4) Intersection (divide) 
> > 5) Cardinality (Existence quantifier) 
> > 6) Cartesian Product (Universal quantifier) 
> > 
> > Of the six operators above, this Toto Space is perhaps the most important because it is the entire geometry in which these six operators work in, and on top of that, it is this operator that provides motion in geometry to form geometry figures. The motion is a "spin".
> > 
> > So, we have a lot of work to do on this last but important operator.
> > 
> > Now the Toto Space Product is truly a product, and for 10 Grid would be this--- first we list all of 10 Grid
> > 
> > 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, ... , 9.8, 9.9, 10.0
> > 
> > Here we did it for 8 year olds in chapter 1, lesson 1-1
> > 
> > 9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
> > 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
> > 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
> > 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
> > 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
> > 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
> > 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
> > 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
> > 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
> > 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 
> > 
> > If we do not count 0.0 then there are 10 x 10 = 100 numbers there in the 10 Grid. But, the Toto Space Product of 10 Grid is 10^2 = 100 and all of the numbers in 100 Grid.
> > 
> > 100 Grid numbers are these
> > 
> > 0.00, .01, .02, .03, .... , 99.98, 99.99, 100.00
> > 
> > Not counting 0.00, how many numbers are there in 100 Grid? Well, there are 100 integers and there are 100 decimal fractions between any two consecutive or successor integers. That means, say, between 1 and 2 there are 100 decimal fractions, between 2 and 3 there are 100 decimal fractions. So between 0 and 100 there are 100 integers and between any two consecutive integers there are 100 decimal fractions, hence, 100 x 100 = 10,000.
> > 
> > So, the Toto Space of 10 Grid is 10,000 numbers.
> > 
> > The Toto Space of 10 Grid is 10,000 numbers yet we only see 100 of those numbers on the x-axis. So where did the 10,000 - 100 = 9,900 other numbers go? 
> > 
> > So in 10 Grid we have 100 points on a graph for x-axis. Yet the Toto Space of 10 Grid is 10,000 points on x-axis. Those other 9,900 points such as 10.01, 10.02, 10.03, . . . 99.98, 99.99, 100.00 are curling back around to 0 in a circle.
> > 
> > More later,....
> > 
> > AP
> 
> Re: let's do hydrogen Re: CO2 has two isomers, and plants only can use animal CO2
> 
> - show quoted text -
> Happy to annouce, that since Google does not engineer a fair level playing field of its Newsgroups, by giving original authors the ability to delete not only their post, but any stalker posts within their own thread-- make original authors, the owners of their thread and the power to delete stalker posts. Happy to announce I will Reverse Engineer what Google should engineer. Thus, all my posts from now on, until Google does the right thing in engineering the delete key to original authors. All my posts will be reincarnated and other deleted as stalking poopers attempt to bully force AP out. 
> 
> An unfair system of discourse deserves unfair habits. Not a level playing field-- a field stacked in favor of persistent bullies whose only goal is to remove a poster and not do math nor physics. 
> 
> This saves me distraction and anger, but it does lose me time. It is worth it for all future posters of science and math and physics. That, as they run into hatemongering stalkers, that they have a choice of actions, other than be forced to leave. 
> 
> So, from now on, all my science, math, physics posts are posted and if a stalker invades, those are resurrected anew and the other one deleted. 
> 
> So, let's do it. 
> 
> AP

Dear Professor Plutonium

I read your posts with great interest and would like to have a better understanding of your ideas. I have a few questions for you:

1. You claim that ovals are conics, not ellipses. I read proofs that ellipses are indeed conic sections. Where is the flaw in these proofs? What makes your proof better?

2. You often refer to experiments in your posts. Does it mean tha true mathematics as you teach it is an experimental science? I've always been told that mathematics was an exact science.

Regards

Someone who wants to know what true mathematics is...

[toc] | [prev] | [next] | [standalone]

#413405 — Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

On Saturday, May 19, 2018 at 1:44:40 PM UTC-5, True Mathematics Learner wrote:
> On May 18 2018, Archimedes Plutonium wrote:
> > On Thursday, May 17, 2018 at 11:45:04 PM UTC-5, Archimedes Plutonium wrote:
> > > #3-8  Toto Space Product in Geometry Logic// Teaching True Mathematics
> > > 
> > > GEOMETRY LOGIC = Set theory 
> > >   
> > > 1) Toto Space Product (multiply) 
> > > 2) Union (add) 
> > > 3) Set Difference (subtract) 
> > > 4) Intersection (divide) 
> > > 5) Cardinality (Existence quantifier) 
> > > 6) Cartesian Product (Universal quantifier) 
> > > 
> > > Of the six operators above, this Toto Space is perhaps the most important because it is the entire geometry in which these six operators work in, and on top of that, it is this operator that provides motion in geometry to form geometry figures. The motion is a "spin".
> > > 
> > > So, we have a lot of work to do on this last but important operator.
> > > 
> > > Now the Toto Space Product is truly a product, and for 10 Grid would be this--- first we list all of 10 Grid
> > > 
> > > 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, ... , 9.8, 9.9, 10.0
> > > 
> > > Here we did it for 8 year olds in chapter 1, lesson 1-1
> > > 
> > > 9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
> > > 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
> > > 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
> > > 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
> > > 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
> > > 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
> > > 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
> > > 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
> > > 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
> > > 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 
> > > 
> > > If we do not count 0.0 then there are 10 x 10 = 100 numbers there in the 10 Grid. But, the Toto Space Product of 10 Grid is 10^2 = 100 and all of the numbers in 100 Grid.
> > > 
> > > 100 Grid numbers are these
> > > 
> > > 0.00, .01, .02, .03, .... , 99.98, 99.99, 100.00
> > > 
> > > Not counting 0.00, how many numbers are there in 100 Grid? Well, there are 100 integers and there are 100 decimal fractions between any two consecutive or successor integers. That means, say, between 1 and 2 there are 100 decimal fractions, between 2 and 3 there are 100 decimal fractions. So between 0 and 100 there are 100 integers and between any two consecutive integers there are 100 decimal fractions, hence, 100 x 100 = 10,000.
> > > 
> > > So, the Toto Space of 10 Grid is 10,000 numbers.
> > > 
> > > The Toto Space of 10 Grid is 10,000 numbers yet we only see 100 of those numbers on the x-axis. So where did the 10,000 - 100 = 9,900 other numbers go? 
> > > 
> > > So in 10 Grid we have 100 points on a graph for x-axis. Yet the Toto Space of 10 Grid is 10,000 points on x-axis. Those other 9,900 points such as 10.01, 10.02, 10.03, . . . 99.98, 99.99, 100.00 are curling back around to 0 in a circle.
> > > 
> > > More later,....
> > > 
> > > AP
> > 
> > Re: let's do hydrogen Re: CO2 has two isomers, and plants only can use animal CO2
> > 
> > - show quoted text -
> > Happy to annouce, that since Google does not engineer a fair level playing field of its Newsgroups, by giving original authors the ability to delete not only their post, but any stalker posts within their own thread-- make original authors, the owners of their thread and the power to delete stalker posts. Happy to announce I will Reverse Engineer what Google should engineer. Thus, all my posts from now on, until Google does the right thing in engineering the delete key to original authors. All my posts will be reincarnated and other deleted as stalking poopers attempt to bully force AP out. 
> > 
> > An unfair system of discourse deserves unfair habits. Not a level playing field-- a field stacked in favor of persistent bullies whose only goal is to remove a poster and not do math nor physics. 
> > 
> > This saves me distraction and anger, but it does lose me time. It is worth it for all future posters of science and math and physics. That, as they run into hatemongering stalkers, that they have a choice of actions, other than be forced to leave. 
> > 
> > So, from now on, all my science, math, physics posts are posted and if a stalker invades, those are resurrected anew and the other one deleted. 
> > 
> > So, let's do it. 
> > 
> > AP
> 
> Dear Professor Plutonium
> 
> I read your posts with great interest and would like to have a better understanding of your ideas. I have a few questions for you:
> 
> 1. You claim that ovals are conics, not ellipses. I read proofs that ellipses are indeed conic sections. Where is the flaw in these proofs? What makes your proof better?
> 
> 2. You often refer to experiments in your posts. Does it mean tha true mathematics as you teach it is an experimental science? I've always been told that mathematics was an exact science.
> 
> Regards
> 
> Someone who wants to know what true mathematics is...

Conics = oval, 2 proofs, synthetic, analytic

Synthetic Geometry & Analytical Geometry Proofs that Conic section =
Oval, never an ellipse-- World's first proofs thereof
by Archimedes Plutonium
_Synthetic Geometry proofs that Cylinder section= Ellipse// Conic section= Oval

First Synthetic Geometry proofs, later the Analytic Geometry proofs.

Alright I need to get this prepared for the MATH ARRAY of proofs, that
the Ellipse is a Cylinder section, and that the Conic section is an
oval, never an ellipse

PROOF that Cylinder Section is an Ellipse, never a Oval::
I would have proven it by Symmetry. Where I indulge the reader to
place a circle inside the cylinder and have it mounted on a swivel, a
tiny rod fastened to the circle so that you can pivot and rotate the
circle. Then my proof argument would be to say--when the circle plate
is parallel with base, it is a circle but rotate it slightly in the
cylinder and determine what figure is produced. When rotated at the
diameter, the extra area added to the upper portion equals the extra
area added to bottom portion in cylinder, symmetrical area added,
hence a ellipse. QED

Now for proof that the Conic section cannot be an ellipse but an oval,
I again would apply the same proof argument by symmetry.

Proof:: Take a cone in general, and build a circle that rotates on a
axis. Rotate the circle just a tiny bit for it is bound to get stuck
or impeded by the upward slanted walls of the cone. Rotate as far as
you possibly can. Now filling in the area upwards is far smaller than
filling in the area downwards. Hence, only 1 axis of symmetry, not 2
axes of symmetry. Define Oval as having 1 axis of symmetry. Thus a
oval, never an ellipse. QED

The above two proofs are Synthetic Geometry proofs, which means they
need no numbers, just some concepts and axioms to make the proof work.
A Synthetic geometry proof is where you need no numbers, no coordinate
points, no arithmetic, but just using concepts and axioms. A Analytic
Geometry proof is where numbers are involved, if only just coordinate
points.

Array:: Analytic Geometry proof that Cylinder section= Ellipse//Conic
section = Oval, never ellipse

Now I did 3 Experiments and 3 models of the problem, but it turns out
that one model is superior over all the other models. One model is the
best of all.

That model is where you construct a cone and a cylinder and then
implant a circle inside the cone and cylinder attached to a handle so
that you can rotate the circle inside. Mine uses a long nail that I
poked holes into the side of a cylinder and another one inside a cone
made from heavy wax paper of magazine covers. And I used a Mason or
Kerr used lid and I attached them to the nail by drilling two holes
into each lid and running a wire as fastener. All of this done so I
can rotate or pivot the circle inside the cylinder and cone. You need
a long nail, for if you make the models too small or too skinny, you
lose clarity.

ARRAY, Analytic Geometry Proof, Cylinder Section is a Ellipse::


              E
             __
      .-'              `-.
    .'                    `.
  /                         \
 ;                           ;
| G          c              | H
 ;                           ;
  \                         /
   `.                     .'
      `-.    _____  .-'
                F

The above is a view of a ellipse with center c and is produced by the
Sectioning of a Cylinder as long as the cut is not perpendicular to
the base, and as long as the cut involves two points not larger than
the height of the cylinder walls. What we want to prove is that the
cut is always a ellipse, which is a plane figure of two axes of
symmetry with a Major Axis and Minor Axis and center at c.

Side view of Cylinder EGFH above with entry point cut at E and exit
point cut at F and where c denotes the central axis of the cylinder
and where x denotes a circle at c parallel with the base-circle of
cylinder

|                              |
|                              | E
|                              |
|                              |
|x            c              |x
|                              |
|                              |
|                              |
|F                            |
|                              |
|                              |
|                              |


So, what is the proof that figure EGFH is always an ellipse in the
cylinder section? The line segment GH is the diameter of the circle
base of cylinder and the cylinder axis cuts this diameter in half such
that Gc = cH. Now we only need to show that Fc = cE. This is done from
the right triangles cxF and cxE, for we note that by Angle-Side-Angle
these two right triangles are congruent and hence Fc = cE, our second
axis of symmetry and thus figure EGFH is always an ellipse. QED



Array proof:: Analytic Geometry proof that Conic section= Oval// never ellipse

ARRAY, Analytic Geometry Proof, Conic Section is a Oval, never an ellipse::


         A
      ,'"   "`.
   /            \
C |     c       | D
 \               /
    ` . ___ .'
         B

The above is a view of a figure formed from the cut of a conic with
center c as the axis of the cone and is produced by the Sectioning of
a Cone as long as the cut is not perpendicular to the base, and as
long as the cut is not a hyperbola, parabola or circle (nor line).
What we want to prove is that this cut is always a oval, never an
ellipse. An oval is defined as a plane figure of just one axis of
symmetry and possessing a center, c, with a Major Diameter as the axis
of symmetry and a Minor Diameter. In our diagram above, the major
diameter is AB and minor diameter is CD.

Alright, almost the same as with Cylinder section where we proved the
center was half way between Major Axis and Minor Axis of cylinder,
only in the case of the Conic, we find that the center is half way
between CD the Minor Diameter, but the center is not halfway in
between the Major Diameter, and all of that because of the reason the
slanted walls of the cone cause the distance cA to be far smaller than
the distance cB. In the diagram below we have the circle of x centered
at c and parallel to base. The angle at cx is not 90 degrees as in
cylinder. The angle of cAx is not the same as the angle cBx, as in the
case of the cylinder, because the walls of the cone-for line segments-
are slanted versus parallel in the cylinder. Triangles cAx and cBx are
not congruent, and thus, the distance of cA is not equal to cB,
leaving only one axis of symmetry AB, not CD.

     /  \A
 x/  c  \x
B/         \

Hence, every cut in the Cone, not a hyperbola, not a parabola, not a
circle (not a line) is a Oval, never an ellipse.

QED

--Archimedes Plutonium

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