@yataqii: What happens when you roll a SQUARE? ⬛ Most people know the Cycloid—the beautiful curve traced by a rolling circle. But what if the “wheel” is a square instead of a circle? In this video, we not only visualize the fascinating polygonal cycloid formed by a rolling square, but also go one step further—can we find the AREA under this curve? 🤯 Unlike the smooth cycloid, this path is made of arcs and sharp transitions. By breaking it into segments, we can actually compute the total area formed in one full rotation. Is the area larger than the square itself? Does it follow a pattern like the classical cycloid? Watch till the end to uncover the math behind it! #MathVisuals #Geometry #Mathematics #STEM #animation
The area is composed of three quarter circles and two right isosceles triangles. 1/4pi + 1/4pi + 1/2pi + 1/2 + 1/2 = pi + 1
2026-04-04 20:26:53
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martinp.v4 :
2LemonPi^2
2026-04-04 17:20:55
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JeffK :
If the square is 1 unit, the left and right pieces are quarter-circles with radius 1, while the center is a quarter-circle with radius sqrt(2) and two triangles that are each half of the square. Total area: (2+sqrt(2))pi / 4 + 1 ≈ 3.681517
2026-04-05 23:44:02
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Bofin :
If the side length of the square is L, then the traced area is (π+1)L^2
2026-04-06 15:09:13
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mesao :
there are three quarter circles, therefore
1) πl²/4
2) ?² = l² + l² ? = l√2
2πl²/4
3) πl²/4
4) πl²/4 + πl²/4 + 2πl²/4 = 4πl²/4 = πl²
just write the dynamical system as a function of t, x,y= coordinate of point @ rotation matrix + velocity, and link theta to the rotation of each corner of the square, split into functions, integrate piecewise probably
2026-04-04 17:51:58
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ur mom :
π-2((π/4)-½)+π/2 = π + 1
2026-04-05 06:54:45
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SangerRainsford :
I did it by hand: A = (3π/4) L^2
2026-04-04 20:22:45
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ignorancia de la tierra :
El área del ♦ rombos?🤔
2026-04-12 15:26:25
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