in order for the straight lines to be 90 deg with the circles, they must be radii of circles with same central point
the length of an arc is defined as c = r * θ (where r is the radius, and θ is the angle)
we define the inner circle with radius r₁ and its arc L₁ = r₁ * θ₁
we define the outer circle with radius r₂ and its arc L₂ = r₂ * θ₂
Because of (1), θ₁ + θ₂ = 2π
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.
Solution:
Explanation:
in order for the straight lines to be 90 deg with the circles, they must be radii of circles with same central point
the length of an arc is defined as c = r * θ (where r is the radius, and θ is the angle)
we define the inner circle with radius r₁ and its arc L₁ = r₁ * θ₁
we define the outer circle with radius r₂ and its arc L₂ = r₂ * θ₂
Because of (1), θ₁ + θ₂ = 2π
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.
Why point (5)?