An original dynamic proof of the late John Conway's Circle Theorem. Sadly, John died in 2020 from Covid 19. He has been described by fellow Mathematicians as a creative genius.
This delighful proof was mentioned by Burkard Polster of Mathloger fame in is Gathering for Gardner talk 'Animating Conway' given on 18th October or 19 October depending on your time zone
Well every geometry proof can be done in the same way. Even though this video isnt a rigorous "proof", just a visualisation needing a proof accompanying it.
This one comes from the book, indeed. I would put an arrow on the spinning colored segment to show that it points in the opposite direction once it makes its way back to its original position. This would make clear that it had to bisect itself since it falls onto itself. If the small circle has radius, r, the colored segments have length, L, then the big circle has radius, R, equal to sqrt((L/2)^2 + r^2)
2 sides converge on each vertex in a triangle. If you extend those sides by the length of the side opposite to the vertex, you can draw a circle with a centre that also happens to be the triangle's incentre
Conway and his proof are indeed amazing, but unless you're already familiar with it, this is just some royalty-free music with colored circles and lines. The animation is good, but this video would have been so much better with at least a brief description, as other commenters have already observed. So, for the simultaneously uninitiated and curious, and at I think about a middle school geometry level: The basic idea here is that, starting with the smaller triangle, if you extend each line by the length of the opposite side from each vertex (per the matching line colors, here), the endpoints of those six new line segments lie on a circle (named a Conway circle). Very neat and elegant proof. I don't know if it's been useful anywhere, but it's a very elegant result in its own right from a legend in math.
This delighful proof was mentioned by Burkard Polster of Mathloger fame in is Gathering for Gardner talk 'Animating Conway' given on 18th October or 19 October depending on your time zone
The video of that was put up on YT yesterday, so expect more visitors here. That's where I came from!
ua-cam.com/video/VrXnwmyxylg/v-deo.html
Thanks!
What is the theorem and what is the proof ?
Lots of information online about the theorem...this is a proof.
Also came here from Burkard Polster's site as a result of a talk he gave on John Conway proofs. Really love your animation here!
Wow, a full proof without words, numbers, letters or symbols in 0:48 !
Thanks!
...or proof, or even a theorem.
Well every geometry proof can be done in the same way. Even though this video isnt a rigorous "proof", just a visualisation needing a proof accompanying it.
Awesome proof! So beautiful!
Thanks!
Love this one. Thanks for it!
This one comes from the book, indeed. I would put an arrow on the spinning colored segment to show that it points in the opposite direction once it makes its way back to its original position. This would make clear that it had to bisect itself since it falls onto itself. If the small circle has radius, r, the colored segments have length, L, then the big circle has radius, R, equal to sqrt((L/2)^2 + r^2)
Nice proof. This music gave me Kung Fu Panda vibes.
Beautiful, please don't give up keep doing what you do it's beautiful
Absolutely wonderfuly, thank you
What is the theorem about? You should put the theorem in the description else those unaware won't be able to comprehend.
Great
I don’t understand this. What is the theorem being proved?
What does it proof?
2 sides converge on each vertex in a triangle. If you extend those sides by the length of the side opposite to the vertex, you can draw a circle with a centre that also happens to be the triangle's incentre
Have you trisected an angle yet though 😂
Conway and his proof are indeed amazing, but unless you're already familiar with it, this is just some royalty-free music with colored circles and lines. The animation is good, but this video would have been so much better with at least a brief description, as other commenters have already observed.
So, for the simultaneously uninitiated and curious, and at I think about a middle school geometry level: The basic idea here is that, starting with the smaller triangle, if you extend each line by the length of the opposite side from each vertex (per the matching line colors, here), the endpoints of those six new line segments lie on a circle (named a Conway circle).
Very neat and elegant proof. I don't know if it's been useful anywhere, but it's a very elegant result in its own right from a legend in math.
Thank you. I still don't see the proof in this animation, but it's nice to have at least a theorem.
Proof without knowing what you need to prove👏🏿👏🏿👏🏿
Conway's circle theorem
All the sudden, my mind was blown.