Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
| From | moroney@world.std.spaamtrap.com (Michael Moroney) |
|---|---|
| Newsgroups | sci.math, sci.physics |
| Subject | Re: 8-teaching Logic in Grade School, TEACHING TRUE MATHEMATICS |
| Date | 2018-05-25 20:29 +0000 |
| Organization | The World : www.TheWorld.com : Since 1989 |
| Message-ID | <pe9ro5$9rm$4@pcls7.std.com> (permalink) |
| References | <fb7b5db1-f161-4236-a449-f5c541edcd6c@googlegroups.com> <9f5d5ab4-c0f2-4cd7-a19b-b3ba3276ef09@googlegroups.com> <cc1efedd-4fa2-43bf-abb1-0cd97fd9eb39@googlegroups.com> |
Cross-posted to 2 groups.
Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:
>#3-9 Many examples and exercises in using Algebraic Logic // Teaching
>True Mathematics
>These last two lessons are going to be long lessons
Here is some True Mathematics which will probably become long lessons:
Below you will find a simple *proof* that shows that certain conic
sections are ellipses.
Some preliminaries:
Top view of the conic section and depiction of the coordinate system used
in the proof:
^ x
|
-+- <= x=h
.' | `.
. | .
| | |
' | '
`. | .'
y <----------+ <= x=0
Cone (side view):
.
/|\
/ | \
/b | \
/---+---' <= x = h
/ |' \
/ ' | \
/ ' | \
x = 0 => '-------+-------\
/ a | \
Proof:
r(x) = a - ((a-b)/h)x and d(x) = a - ((a+b)/h)x, hence
y(x)^2 = r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h/2)^2/h^2.
Hence (1/ab)y(x)^2 + (4/h^2)(x - h/2)^2 = 1 ...equation of an ellipse
qed
Back to sci.math | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread
8-teaching Logic in Grade School, TEACHING TRUE MATHEMATICS// Maximum Electric Coil theory-- how inside of atoms works Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-23 19:27 -0700
Toto Crappo for the 8th time.. you rock AP! alouatta.coibensis@gmail.com - 2018-05-23 20:28 -0700
Re: 8-teaching Logic in Grade School, TEACHING TRUE MATHEMATICS Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 10:53 -0700
#3-9 Many examples and exercises in using Algebraic Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 22:20 -0700
Re: #3-9 Many examples and exercises in using Algebraic Logic // AP confuses himself alouatta.coibensis@gmail.com - 2018-05-25 07:40 -0700
Alouatta says Caltech does not know a cone from a hole in the ground--Matthias Flach Anton N. Kapustin Alexander Kechris never able to do true-Calculus or understand Proton = 840MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 11:01 -0700
#3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 23:16 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-26 09:56 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-26 10:25 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-27 07:59 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics alouatta.coibensis@gmail.com - 2018-05-27 08:10 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-27 13:02 -0700
Re: #3-10 Many examples and exercises in using Geometry Logic // Teaching True Mathematics bursejan@gmail.com - 2018-05-27 13:04 -0700
Re: 8-teaching Logic in Grade School, TEACHING TRUE MATHEMATICS moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-25 20:29 +0000
Re: 8-teaching Logic in Grade School, TEACHING TRUE MATHEMATICS// Maximum Electric Coil theory-- how inside of atoms works bursejan@gmail.com - 2018-05-27 13:00 -0700
csiph-web