Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.physics > #687086

Re: Alouatta says Caltech does not know a cone from a hole in the ground--Michael Aschbacher, Alexei Borodin, Danny Calegari never able to do true-Calculus or understand Proton = 840MeV

Cross-posted to 2 groups.

Show all headers | View raw

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

>Alouatta says Caltech does not know a cone from a hole in the 
>ground--Michael Aschbacher, Alexei Borodin,  Danny Calegari never able to 
>do true-Calculus or understand Proton = 840MeV

Even if Archie can't tell a cone from a hole in the ground, he should be
able to understand this proof that the ellipse is a conic section.

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.physics | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

page1&2 True Chemistry-- 2018 textbook of Experiment-- Real Electron = 105MeV, Real Proton = 840MeV, Dirac's magnetic monopole = .5MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 09:46 -0700
  page3&4 True Chemistry-- 2018 textbook of Experiment-- Real Electron = 105MeV, Real Proton = 840MeV, Dirac's magnetic monopole = .5MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 10:47 -0700
    page5&6 True Chemistry-- 2018 textbook of Experiment-- Real Electron = 105MeV, Real Proton = 840MeV, Dirac's magnetic monopole = .5MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 19:11 -0700
      page7&8 True Chemistry-- 2018 textbook of Experiment-- Real Electron = 105MeV, Real Proton = 840MeV, Dirac's magnetic monopole = .5MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 20:53 -0700
        page9&10 True Chemistry-- 2018 textbook of Experiment-- Real Electron = 105MeV, Real Proton = 840MeV, Dirac's magnetic monopole = .5MeV Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 17:57 -0700
  Re: Alouatta says Caltech does not know a cone from a hole in the ground--Michael Aschbacher, Alexei Borodin, Danny Calegari never able to do true-Calculus or understand Proton = 840MeV moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-25 20:14 +0000
    Re: Alouatta says Caltech does not know a cone from a hole in the ground--Michael Aschbacher, Alexei Borodin, Danny Calegari never able to do true-Calculus or understand Proton = 840MeV benj <benj@nobody.net> - 2018-05-25 18:14 -0400

csiph-web