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35,406 Views • May 7, 2023 • Click to toggle off description
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualProofs. Thanks!
This animation is based on a proof by Roger B. Nelsen from the January 2015 issue of The College Mathematics Journal page 10 (doi.org/10.4169/college.math.j.46.1.10 ).
After I created this, I found another wonderful animation of this same visual proof : • Area of dodecagon | Beautiful geometr... (though the animator there does not cite the original visual proof from Nelsen).
#math #manim #visualproof #mathvideo #geometry #mathshorts #geometry #mtbos #animation #theorem #pww #proofwithoutwords #proof #iteachmath #dodecagon #area #dissection
To learn more about animating with manim, check out:
manim.community/
Views : 35,406
Genre: Education
License: Standard YouTube License
Uploaded At May 7, 2023 ^^
warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
Rating : 4.995 (3/2,541 LTDR)
99.88% of the users lieked the video!!
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User score: 99.82- Masterpiece Video
RYD date created : 2024-05-21T19:20:22.446727Z
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39 Comments
Top Comments of this video!! :3
There's also something kind of neat about the dodecagon being cut into 12 pieces, and the squares each being made of 4 pieces
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Another lovely visualization explicated
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This is why the formula for the area of a circle is (pi)(r)^2. Because pi is very close to 3r^2 which is how you find the area of this shape!!!! So cool!!!
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Umbrella ?
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Wow, this is really well done. Thank you for this gem <3
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Would you ever consider doing a visual representation of Laplace transformations? Perhaps illustrating it in the context of Routh-Hurwitz stability criterion?
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We might not be able to square the circle, but at least we can cube the regular dodecahedron 🤷♂
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Let me just mention the channel "Think twice" here, they also did this proof a few years ago in a similar style
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Wow😍
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Wait so does that mean the generic formula is 3r^2?
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What's the great music called?
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Good, a visual proof that is actually proved with visuals alone. Unlike that last one you made with the peeling of the circle to find the area which was not proof, only an illustration whish need mathematical proof to support it. This proof needs no maths to support it, we can all see and understand exactly how the areas are equal.
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Editing software name?
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Area of circle =3x(radius) ^2+ 0.14..... plzz give heart & I found that circumference of circle=Radius/0.1591549......
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@caspermadlener4191
1 year ago
Wow, this method is even better than the short making a square with side length √3, since it doesn't use Pythagoras.
And that was already one of my favourite videos!
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