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82,608 Views • Jun 6, 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!
For a longer (and more dramatic, large version see • Area of a Regular Dodecagon II (visua... ).
This animation is based on a dissection by J. Kürschák that appears in the following sources:
Mathematical Morsels by Ross Honsberger (MAA, 1978)
Proofs without Words II by Roger B. Nelsen (MAA, 2000) (bookstore.ams.org/clrm-14/)
#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 : 82,608
Genre: Education
License: Standard YouTube License
Uploaded At Jun 6, 2023 ^^
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Rating : 4.844 (200/4,925 LTDR)
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RYD date created : 2024-10-24T21:24:56.665825Z
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106 Comments
Top Comments of this video!! :3
Clarification: The dodecagon's area can be expressed as the sum of three squares, with each square having a side length equal to half the radius of the dodecagon.
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Beautiful! The proof can be derived with Mid level Trigonometry. Area of Dodecagon expressed in terms of the radial drawn from the centre. The radii form 12 congruent isosceles triangles with Apex angles of 30 degrees each. Area of Dodecagon equals 12 times the area of the triangle. Using trigonometry the Radius r and side s can be shown to be related as r^2 = (2 + sqrt 3) s^2.
Area of each triangle in terms if side s equals s^2 (2 + sqrt 3)/4
Area of Dodecadron equals 12 times area of triangle = 3 s^2(2 + sqrt 3), which in terms of radius r = 3r^2
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Beauty was promised and beauty was delivered.
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I love visual math
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Your videos makes me want to relearn math sincerely. Someday I might. Keep making this videos. Appreciate it❤
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really beautiful proof
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Excellent, but yet to prove that those two brown and one purple triangles exactly fill up the gap in each quadrant (that those triangles have not been manipulated during animation).
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beautiful piano rendition of the interstellar theme
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Beautiful
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Awesome. I did compute it and arrived at 12(cos 15)(sin 15) which is 3.
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Mind blowing channel you got one more subscriber
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This is calculated by the formula: sin(π/n)×cos(π/n)×n, where n is the number of sides
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That's beautiful but I'm gonna have to write out the equations for a while to understand the proof of why those shapes really do fit into those spaces
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My head exploded
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A=d^2*3/4
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What engineers think circles look like
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Mind blown!
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= 3r²
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if school show us things like this, everyone will be the next Einstein
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@vladimirrodriguez6382
1 year ago
Summarizing the area of the regular dodecagon is equal to 3/4 of the area of the circumscribed square. What a beautiful visual proof
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