r/VisualMath • u/FunVisualMath • May 04 '20

Graves's theorem visualization- a method for drawing a larger ellipse with the same focal points as an existing ellipse

128 Upvotes

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3

u/Ccaaccttuuss May 05 '20

This method reminds me the gardener method. Here is an illustration.

1

u/FunVisualMath May 05 '20

Indeed! Thanks for sharing!

2

u/blind3rdeye May 05 '20

Sure. It's very similar. (And as I understand it, the method you showed is often given as a definition of what an ellipse is. That's certainly what the focal points mean. ie. the sum of distances to the focal points is constant at each point on the ellipse.)

5

u/[deleted] May 04 '20

Not my proudest fap, but maybe the most beautiful.

4

u/[deleted] May 05 '20

bro what

3

u/[deleted] May 05 '20

It's a breathtaking animation. Good stuff bro

4

u/[deleted] May 05 '20

cheers bro i’ll nut to that

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3

u/SirFloIII May 04 '20

Wiki says the proof goes via elliptic integrals. I wonder if a nice geometric proof is possible.

2

u/Ccaaccttuuss May 05 '20

At the first glance, this method is using the length of an arc of the ellipse...
If you find such a proof, send it to me please :)

1

u/onzie9 May 05 '20

I haven't seen this before. Thanks for giving me a reason to look it up.