this post was submitted on 08 Jun 2025
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Learned this one in 6th grade geometry: drawing a square in thr corner doesn't make it 90°
But these are all right angles, as long as the two arcs are centered on the same point as the intersection of the two straight lines.
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Dammit Diogenes, this is why we don't allow you in the geometry class anymore.
Solution:
Explanation:
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in order for the straight lines to be 90 deg with the circles, they must be radii of circles with same central point
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the length of an arc is defined as c = r * θ (where r is the radius, and θ is the angle)
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we define the inner circle with radius r₁ and its arc L₁ = r₁ * θ₁
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we define the outer circle with radius r₂ and its arc L₂ = r₂ * θ₂
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Because of (1), θ₁ + θ₂ = 2π
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To create the shape, L₁ = L₂ = r₂ - r₁
If you start replacing and solving, you will get a 2nd grade quadratic, which has a positive and a negative solution. The positive solution is that magic number.
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