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Tractrix demonstration: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed

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  Tractrix demonstration: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-02 19:40 -0800
    Tractrix demonstration: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-02 20:42 -0800
      Tractrix demonstration: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-03 10:06 -0800
        highlighting some ideas Re: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-03 20:08 -0800
          geometry in High School Re: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-03 20:31 -0800
            Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-03-04 06:50 +0000

#436058 — Tractrix demonstration: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed

#5-3  tractrix demonstration with pocketwatch

Newsgroups: sci.math
Date: Sat, 4 Aug 2018 22:09:07 -0700 (PDT)

Subject: Tractrix demonstration-- pocketwatch pulled by chain //TEACHING TRUE MATH
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sun, 05 Aug 2018 05:09:07 +0000

Tractrix demonstration-- pocketwatch pulled by chain //TEACHING TRUE MATH

Alright, earlier I wrote about Wikipedia's tractrix in motion. That will be impractical for classroom. On Youtube shows a x and y axis with dragging a pocketwatch placed at (0,1) of a large graph paper and dragging it along the x axis, to form a 1/2 horn figure. This pocketwatch dragging is a nice experiment to show the class. 

The pocketwatch so as to outline the curve dragged across the graph paper. 

The Tractrix path is the path of least resistance. 


On Friday, August 3, 2018 at 11:48:40 PM UTC-5, Archimedes Plutonium wrote: 
teachers and students will love this textbook -- so universal, so logical Re: _4-4 exercises with Calculus//TEACHING TRUE MATHEMATICS, 2018 

Now one of the great advantages of this textbook, not only is it the first math text written logically, but the first math textbook that is used throughout education-- where no other math book is needed. And the great advantage of that, is in case a student moves, they have no worries as to being behind in math, because their next school will be using the same textbook. And I want my textbook to be the first international used math textbook for ages 8 to 26. So no matter where on Earth you go, if you want to know whether you are behind or ahead of the "rest of the pack" in math, just look at where you are in AP's textbook. 

And teachers, once they get into the swing of this textbook will just love it, because every day is charted out for them, what they must cover and what they have to teach. And then, that gives the teachers opportunities to make special teaching aids, hands-on experiments-- such as the Calculus rectangle trapezoid or the Pythagorean theorem cut out. Or the Globe with "stick-um" Grid numbers explaining Toto Space Product. 

Or, like the Tractrix demonstration that I want the teacher to especially do well with. Look at Wikipedia "tractrix" with its tractrix in motion. For I want the teacher to do this demonstration in class and for the students to do it at home and then in class the next day. 

Wikipedia-- demonstration Tractrix by dragging a pole 

So the teacher has to have the demonstration all worked out and give students guidance what they should use. Perhaps explore the internet for someone with a good practical way of making the tractrix. 



On Monday, August 20, 2018 at 6:30:51 PM UTC-5, Archimedes Plutonium wrote:
89Talk 1-12 tractrix verification // TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium


Alright, pocketwatches have arrived and place a graph paper onto the inside of a cardboard box in order to use as a straightedge along one side. 

At x=1, mine is near to .35. 

On Monday, August 20, 2018 at 6:44:53 PM UTC-5, Archimedes Plutonium wrote:

I think .35 is close to the truth. 

One good news is that it is not a two person operation, and no need to build a special tool that marks out the path. We can visualize the center of the pocketwatch and read off where the coordinate points are. 


On Monday, August 20, 2018 at 7:05:37 PM UTC-5, Archimedes Plutonium wrote:

Yes, yes, well looking at Wikipedia's tractrix 

Tractrix with object initially at (4,0) 

And recalibrating, implies that at x=1 , the tractrix arc is a bit over .25. I got .35 crudely. 


Newsgroups: sci.math
Date: Wed, 22 Aug 2018 21:46:02 -0700 (PDT)

Subject: 82Talk -1-19 insights into Tractrix// TEACHING TRUE MATHEMATICS
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Thu, 23 Aug 2018 04:46:02 +0000

82Talk -1-19 insights into Tractrix// TEACHING TRUE MATHEMATICS

82Talk -1-19 insights into Tractrix// TEACHING TRUE MATHEMATICS 

Alright, I have pocketwatches and am able to do the plotting of the graph of the tractrix. Something I want the students to do as a school project and the teacher show them as a class demonstration. 

What I found though is an enticing afterthought. 

The size of the Pocketwatch is going to start to interfer in plotting as we get closer to the x-axis. 

The point of the Tractrix is to spot where Infinity borderline is. This is needed for Calculus.

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#436061

I have till end of this year to finish this first edition and it is taking me too long. So i decided to patch in all the topics i want to cover, and then later smooth them out. It is no mystery that only after many editions will the book be flowing smooth.

It is a dash to the finish before December.

I need to cover area and volume of many geometry figures.

Do the Power Rules of Calculus in High School and finish out High School with converting functions to polynomials— good use of algebra in converting.

That brings me to college freshman calculus where we resume with function conversion to polynomials then develop the AP-Maxwell Equations and spend the rest of the year mastering those equations.

Sophomore, junior, senior years not sure what i want covered.

The heart of math and physics is the AP- Maxwell Equations.

The only thing i can think of that can be covered is “logical thinking and math proving”

Only in New Math proofs are not important. In Old Math proofs meant everthing (sadly). In New Math, proofs are like a dessert such as a after dinner mint. The meat and potatoes of math is the AP-Maxwell Equations.

So sophomore year math is probably advanced AP-Maxwell Equations.

And then i should not forget that some other math like Probability and Statistics should be covered.

It is worth mentioning that AP threw out all these as either fakery or not worthwhile
Trigonometry, topology, fractals, group-ring-field theory, nonEuclidean geometry,Reals irrationals, complex numbers, transcendental b.s.

Discrete math is worthwhile for Grid numbers are discrete.

No need for ordinary and partial differential equations because we have Polynomials.

Somewhere at junior or senior level a rigorous symbolic logic needs be done.

AP

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#436114

Now in this textbook several pages i am going to want to emphasize a key lifelong lesson in math. One of the reasons i had to begin with 5 year olds to save them from math pollution and brainwash. A page devoted to just a key idea, and fill the page with the idea.

You cannot subtract more than what is available. No negative numbers exist.

Another one of these lessons is:

First Quadrant Only. All of math takes place in 1st Quadrant Only.

Another one of these crucial lessons is:

Infinity is a Borderline between finite numbers and infinite numbers.

Another one is:

The only true numbers of mathematics are Grid Numbers.

Try to think of a lesson of the day when the students reach one of these pages. A fun lesson— perhaps the teacher bringing a demonstration to class.

AP

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#436185 — highlighting some ideas Re: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed

On Sunday, March 3, 2019 at 12:06:52 PM UTC-6, Archimedes Plutonium wrote:
> Now in this textbook several pages i am going to want to emphasize a key lifelong lesson in math. One of the reasons i had to begin with 5 year olds to save them from math pollution and brainwash. A page devoted to just a key idea, and fill the page with the idea.
> 
> You cannot subtract more than what is available. No negative numbers exist.
> 

So I like to see a whole entire page with nothing but.

You cannot subtract more than what is available. No negative numbers exist.
You cannot subtract more than what is available. No negative numbers exist.
You cannot subtract more than what is available. No negative numbers exist.
You cannot subtract more than what is available. No negative numbers exist.
.
.
.




> Another one of these lessons is:
> 
> First Quadrant Only. All of math takes place in 1st Quadrant Only.
> 


First Quadrant Only. All of math takes place in 1st Quadrant Only.
First Quadrant Only. All of math takes place in 1st Quadrant Only.
First Quadrant Only. All of math takes place in 1st Quadrant Only.
First Quadrant Only. All of math takes place in 1st Quadrant Only.
.
.
.






> Another one of these crucial lessons is:
> 
> Infinity is a Borderline between finite numbers and infinite numbers.
> 


Infinity is a BORDERLINE between finite numbers and infinite numbers.
Infinity is a BORDERLINE between finite numbers and infinite numbers.
Infinity is a BORDERLINE between finite numbers and infinite numbers.
Infinity is a BORDERLINE between finite numbers and infinite numbers.
.
.
.





> Another one is:
> 
> The only true numbers of mathematics are Grid Numbers.
> 

The only true numbers of mathematics are Grid Numbers.
The only true numbers of mathematics are Grid Numbers.
The only true numbers of mathematics are Grid Numbers.
The only true numbers of mathematics are Grid Numbers.
.
.
.




> Try to think of a lesson of the day when the students reach one of these pages. A fun lesson— perhaps the teacher bringing a demonstration to class.
> 

This is my way of emphasizing ideas, highlighting ideas, to steer students away from pollution and brainwash.

AP

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#436188 — geometry in High School Re: TEACHING TRUE MATHEMATICS, textbook for ages 5 to 26, by Archimedes Plutonium, 2018, 1st ed

Alright, in High School, the geometry class will go through all the most important figures of geometry and derive their area, and volume, and perimeter. My complaint of Old Math geometry in High School-- too much, far far too much on "congruent".

So here I need to look up my past work on this for a date time group and collect and harvest that data.

--- quoting old 2017 post of mine ---


Perfecting the 3 famous proofs;; circle, sphere, areas, volume;; world's finest logical proofs of pi*r^2, 4pi*r^2, 4/3*pi*r^3

me (Archimedes Plutonium change) 	
7/13/17


Not there yet, but close, what I need to correct in the below is that of the method of volume is to move area, move it linearly in space to obtain volume. Once I have that, then I achieved logical perfection on these three proofs 


On Wednesday, July 12, 2017 at 3:18:52 AM UTC-5, Archimedes Plutonium wrote: 
> Yes, this is what I wanted, logical integrity in the proofs of circle area, then sphere area then sphere volume. I want those three proofs, as if they were all contained in one proof. I did not want a proof of one unrelated to the other two. 
> 
> And it pays to take a vacation or break from a pursuit, because when you return, it seems as though the head is clear to do good work. 
> 
> So let me summarize so far:: 

Let me go through this again, for Logic demand a lot of repeating and rehashing until perfect. 
Logic is perfect, and perfection is logic. 

Math, on the other hand is Precision, for precision is math and math is precision. 

Logic is perfection. 

What is Physics? Well, it is all of science. 

> 
> We start with knowing area is from rectangle, length times width 
> 

We start from beginning, define area and it is rectangle, length times width 


> We carry that idea into circle area, so we want a circle turned into a rectangle then take length times width 
> 
> We do that by dissection of circle and reassemble to this 
> 
> |/\/\/\/\| where those are slices out of a circle, 16 slices stacked up forming a rectangle (note also that the 16th section is further cut in half to form a straight line ends) that is pi*r long and r wide for area of pi*r^2 
> 
> Going smooth, real smooth, we go from rectangle to circle area via dissection. 
> 

So we have the first chore done, circle area and we carry forward to sphere area 


> Now we jump to sphere area, everything in logical order, everything done logically. 
> 
> So we notice the sphere and want the area, and naturally we notice the sphere is made up of Great Circles, like the longitude lines and the equator. We ask, how many Great Circles as a quantity composes the surface area of entire sphere? does it take 2 Great Circles, or 3 or 3.5, or 4 or 4.75, or 5 or 6? How many? 
> 

Now if possible, we would like to do to the sphere what we did with circle, cut the sphere up and form some rectangle. But here a huge problem comes in-- the sphere is bent and much of its area is "bent area". So, we need some other way of finding the sphere area. 


> So we estimate by taking two Great Circles, the equator and one line of longitude (some call them meridians). Two Great Circles that split the sphere into 4 dissections called lunes. Did the Ancient Greeks know of the lune? Anyway, we are trying to estimate how many Great Circles is equal to the surface area. We see instantly that the single Great Circle has way more area in its hemisphere than the area of a flat circle of a meridian. But with 2 intersecting Great Circles, the meridian and equator, that 4 lunes are the result. Now a lune, I like to call a Diangle, because a lune to me looks like a two sided triangle, so I call a lune a Diangle. 
> 
> Experiment: at home you probably have a globe of Earth with all the countries and oceans and held up by two metal arms so you can spin the globe in these metal arms. I have one and is using the one arm as the equator and the other as a meridian forming 4 Diangles. 
> 
> So, the proof of sphere area is 4pi*r^2 simply involves recognition that these 4 Diangles, 4 lunes, each lune is equal in area to the Great Circle of that same sphere. Now in my globe, if I close the gap of two arms to make the lune smaller, we see that the area of the lune is smaller than the area of Great circle. We see also that there is some special location of the two arms where the lune area equals the Great Circle area, if we extend further from this equal state, the area of lune is larger. So, is it when the lune is dissecting the sphere into 4 and only 4 lunes, that the Great Circle area equals the lune area? And, how do we prove that? 
> 
> We prove it by knowing the length of the 4 Diangle arc is exactly pi*r, the width of the Diangle is 1/4*pi2*r. The length of the Great Circle turned into rectangle is pi*r and the width is r. So the Diangle width is in excess by pi/2 over the rectangle width of just r. So we can cut this excess of pi/2 off the Diangle top and bottom of its most wide arc. So the two pieces are further divided in half so that we have 4 pieces. These four pieces are joined at the two vertex of the Diangle, forming a rectangle that is now pi*r long and r wide, for area that equals Great Circle area of pi*r^2. And since there are 4 of these Diangles involved, means area of sphere is 4pi*r^2 
> 

In circle area there was dissection, in sphere area, there was dissection of the Diangle to equal the area of Great Circle. 



> Now, continuing to the sphere volume using the facts given so far and using dissection for proof. 
> 
> We notice that a cone has volume of 1/3*pi*r^2*height 
> 

In sphere volume we have the same problem as in sphere area, we have bent space that is hard to lay out into a rectangle or a rectangular solid so we have to employ some other figure to help. In the case of sphere volume we need the help of the cone and the cone needs the help of the square pyramid. 

Volume of Pyramid and Cone:: 

 I am going to take the example of 6 pyramids of 1/2 height tiling the inside of a cube, arguing that we can fill the cylinder with 6 of those 1/2 height cones. Just substituting cone for pyramid. 

Now, the crucial point here is getting 1/6, so that 1/6 is 1/3 times 1/2. Otherwise, trying to visualize 3 pyramids inside a cube is extremely difficult, but 6 half sized pyramids, one for each side makes sense. 

Now, the 6 cones inside a cylinder, yet the cylinder has no 6 walls. So, here, in the Grand Proof of circle area, sphere area, sphere volume, where I need the fact of 1/3 as in 1/3*pi*r^2*height for cone volume to use in sphere volume. Here, to be utmost LOGICAL, and that is the whole point of this exercise, is that I fall back to primal beginnings as with circle area. 

In circle area, we did a dissection, remember:: 

You have a given circle and you section it into 16 equal slices. One of the sections you further cut in half to make the two bookends of the formed rectangle. 

|/\/\/\/\| 

Where those are slices out of a circle, 16 slices stacked up forming a rectangle that is pi*r long and r wide for area of pi*r^2. QED 

Coming out with identical volume formulas 1/3*pi*r^2*height and 1/3*s^2*height respectively 

Surprisingly there is a dissection involved of starting with a cube or cylinder and carving out the 6 objects respectively 


Here, we do another dissection of both a pyramid and a cone, and very much similar to the circle dissection 

|/\/\/\/\| 

Only this time for volume and instead of rectangle area, here we have rectangular-solid volume. 

The sections of pyramid and cone are flat enough to be laid side by side to form a rectangular solid. 

We take our 6 pyramids, slice them in 1/2 forming 12 half pyramids (do the same on cones) 

We then stack them in this pattern 

|/\/\/\/\| 

In effect this pattern is the calculus integration. 

So, the lesson, the 1/3 is never obvious by taking 3 cones or 3 pyramids. What is obvious is taking 6 half sized pyramids, and thus 6 half sized cones. 

Now the reader should feel a sense of duality here in these famous proofs. For circle we had rectangle, for sphere area we had circle area, for sphere volume we had pyramid volume to cone volume, then finally to sphere volume. A duality of going from curved arcs to rectangles and back and forth. 

Could I have bypassed the cone volume to get the 1/3 in 4/3pi*r^3. To answer that, I needed to dissect the sphere and try to assemble the pieces into some rectilinear shaped volume figure. That is extremely hard to do, perhaps it has a reason why so difficult-- the sphere arcs are maximum arcs in some sense of mathematics, so, it is easier to dissect a cone to be rectangle solid shape than it is to dissect a sphere. And that is the whole point of bringing in the cone volume, because making sphere volume flat enough to measure is nay impossible. 

Now, all the above were known, before I did this project, except for one item. One item I take all the credit for. The item I speak of, is the item that I take the two hemispheres of a sphere and see them as two generalized cones. A hemisphere is a cone in a sense. A hemisphere is a bowl, and a bowl is a cone with arc sides. Instead of a cone with a straightline rising height meeting in a apex, a hemisphere is a cone that meets in a pole with arc risers. 

So, I have the cone volume of 1/3pi*r^3. I have a sphere cut in half and each hemisphere volume is a cone volume is 2/3pi*r^3, where the 2 is the 2radii = diameter = height. Since there are 2 of these hemispheres the total volume is 4/3pi*r^3. 

> Here the dissection is the cutting of the sphere into two pieces, two hemispheres and looking at a hemisphere as a cone, a very very round cone. In fact, most would overlook a hemisphere as a cone. 
> So now you have 2 cones, 2 hemispheres, and the height of the two cones is 2r, the base of the cone is pi*r^2 
> The volume of a cone is 1/3*pi*r^3 and since there are two of these we have 2* 2/3*pi*r^3= 4/3*pi*r^3. 
> 

So, the above is a Logical Proof of the three famous area and volumes in geometry, and we had to throw in that of pyramid and cone. 

I believe the above is the world's most simple and easy proofs of these formulas. All other proofs cannot be arranged Logically, but rather scatterbrained. Except for Calculus, because calculus of area and volume is merely a procedure, not an insight into meaning, calculus is a operation which has no meaning for why and what. Like adding 8 and 23, we just add, with no meaning. 

Now there was an item of deep mystery in this, something Calculus could never find or touch upon. The mystery is that volume is often gotten from a technique of knowing the area of a face, and then with height or length we multiply this face area to get volume. This works well on rectangle solids, prisms, cylinder, etc. But for some reason, multiplying a great-circle of a sphere over a given distance does not give the volume. I remarked earlier that this method relies on linear motion in space for the face to provide a volume. That by rotating a great circle in a sphere cannot give its volume. It has to be linear motion. 

But hold on a minute, maybe I talked myself into a proof of sphere area. 

We know the surface area of sphere is 4pi*r^2, and we know the face is the surface area. So if we walk that sphere a distance of 1/3, we should have the volume of the sphere. But what is the meaning of a linear walk of 1/3. The meaning would be, that every point on the surface would have a chance to represent every point of the volume. And the number 1/3 would be 1/3 radius. So, I take a sphere and measure its radius. I draw a straightline of radius and mark 1/3 of it. I place beginning of the sphere on the start mark, then I move the sphere linearly the 1/3 distance. Does every point inside the sphere be at least one time coincide with a surface point? yes indeed. 

So here, in passing comment I found an alternative proof, using linear motion and not needing the cone or pyramid. 

If I take the sphere and move it 1/3 linear distance the surface points will coincide with all interior points and thus be volume. 

So I have surface points as 4pi*r^2 and if I move them through a distance of 1/3 radius, I coincide with all interior points, hence the volume. 

Now, lastly, I need to get the above ready for the Math Array. 

AP

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#436194 — Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test

AlzheimerPlutonium <plutonium.archimedes@gmail.com> fails at math and science:

>So I like to see a whole entire page with nothing but.

>You cannot subtract more than what is available. No negative numbers exist.
>You cannot subtract more than what is available. No negative numbers exist.
>You cannot subtract more than what is available. No negative numbers exist.
>You cannot subtract more than what is available. No negative numbers exist.
>.
>.
>.

WARNING TO PARENTS: Archimedes Plutonium is offering to teach your children
his broken math. BEWARE! He will corrupt the minds of your children! He
teaches there are no negative numbers, no complex numbers, he teaches a
sine wave isn't a sine wave plus many, many other instances of bad math.
In addition, he loves to teach false Boolean logic such as 3 AND 2 = 5.
His method at doing this is particularly insidious. He'll post a false
statement that nobody believes, such as 3 OR 2 = 5, say that it is false,
but then he'll try to replace it with another similar false statement such
as 3 AND 2 = 5, in order to really confuse future computer scientists.
In addition, he appears to be resorting to BRAINWASHING attempts by
needless repetition of his lies.

Nobody knows why he wishes to corrupt the minds of children like this.
Perhaps he wants everyone to be a failure at math, just like he is.
Perhaps he is an agent of Putin and Russia, or maybe of China, in order
to make sure they will continue to dominate the trade economy. But the
point is, stay away, if he offers to give or sell you his dangerous book!

In addition, Plutonium wants to usurp good Christians by trying to convince
students to worship his evil pagan Plutonium atom god.


x-no-archive: yes

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