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| From | moroney@world.std.spaamtrap.com (Michael Moroney) |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: 9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 |
| Date | 2018-05-25 20:10 +0000 |
| Organization | The World : www.TheWorld.com : Since 1989 |
| Message-ID | <pe9qir$9rm$1@pcls7.std.com> (permalink) |
| References | <1098864b-7cc4-427b-a0ab-6278dc9f2eab@googlegroups.com> <32eff521-bca0-4e9c-9138-7d30187a6b8c@googlegroups.com> |
Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:
>9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4
How's this for a breakthrough in conic sections?
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
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9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-23 15:11 -0700
Re: 9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-23 22:14 -0700
Re: 9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-23 22:30 -0700
No, AP, when you slice a cone from the apex, it will lie flat. alouatta.coibensis@gmail.com - 2018-05-24 08:22 -0700
No, fruitcake-- it never lies flat Re: No, AP, when you slice a cone from the apex, it will lie flat. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 09:53 -0700
Poor AP. Can't use use scissors correctly. Holds them at the wrong end. alouatta.coibensis@gmail.com - 2018-05-24 09:59 -0700
AP continues his assault on conic sections alouatta.coibensis@gmail.com - 2018-05-24 08:23 -0700
Re: 9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-25 20:10 +0000
Re: 9TEACHING TRUE MATHEMATICS// Breakthrough in Conic Sections along with Physics//chapter 4 bursejan@gmail.com - 2018-06-24 21:36 -0700
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