OscarSteenstrup

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Hi again. I have been stuck on this for almost 3 hours by now, and i have ran out of ideas..

I am working on a proof called dandelin spheres, which proves you can get an ellipse by cutting a cone with a plane.

I have found the right equation for both semi circles, the line (cone) and the plane.

I have defined the spheres as semi circles, and the cone as a line, which i am plotting by using the surface of revolution command.

The problem lies within the fact, that i cannot use the intersectplot command with surface of revolution, and i need the plot to show the intersection between the plane and cone. 

The following shapes are defined:

cone line - f := x -> 0.5*x;
small sphere - g := x -> sqrt(0.8944271908^2 - (x - 2)^2)

bigger sphere - h := x -> sqrt(3.354101965^2 - (x - 7.5)^2)

plane - m(x, 0) := 1.216350358*x - 3.841106394

with the following command i recieve this output, which i nice, but i am missing the final part, the ellipse.

 

I hope someone can help a desperate student :)

- Oscar

Hello.

I am currently working on a geometric proof, that cutting a cone can give you an ellipse. I have chosen the 'Dandelin spheres' proof, but i am having trouble plotting a hollow cone containing two solid spheres of different sizes. 

I thought i could maybe define each function, and then just display th surface area of the revolution of the cone, and the volume of revolution of the spheres in the same plotting table. However, this has proven more difficult than i thought.

f(x):=0.5*x

g(x):=sqrt(0.81-(x-2)^2)

h(x):=sqrt(3.57^2-(x-8)^2)

display([VolumeOfRevolution(f(x), x = 0 .. 10, output = plot, scaling = constrained), VolumeOfRevolution(g(x), x = 0 .. 10, output = plot, scaling = constrained), VolumeOfRevolution(h(x), x = 0 .. 10, output = plot, scaling = constrained)])

 

(I am aware that i have plotted the cone function (f(x), straight line) as volume and not surface area of revolution)
 

This does not give me one combined plot, but 3 seperate:(

I hope someone has the time to help!
Thank you

Hello

I am currently working on a visual proof that cutting a cone with a plane, can give you a mathematically correct ellipse.
Therefore i want to animate a cone, using the "cone" command, where you can set the origin, radius and height. I was wondering if it is possible to, using the animate command, make an animation with a cone, either chaning radius of base or height. I have tried various combinations of different commands, but have not had any success. I hope you can help me out!

- Oscar

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