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r

 πr

S= π \,r^2

 圆的面积 

t = -2 (slider from -2 to 1, step 0.01)
β = If(t ≤ -1, 45.0001°, t ≥ 0, 89.9999°, (45° * (t + 2)))
r: 1
A: (0, 0)
C: A + (0, (2 * r))
α = If(t ≟ -2, 45.0001°, t ≥ -1, 89.9999°, (45° * (t + 3)))
D: C - (0, (r * tan(β)))
C' = Rotate(C, ((0.5 * π) * r / Distance[D, C]), D)
C'' = Mirror(C', x = 0)
d = CircleArc(D, C'', C')
O: A + (0, r)
B: A + (0, (r * tan(α)))
A' = Rotate(A, ((0.5 * π) * r / Distance[B, A]), B)
A'' = Mirror(A', x = 0)
c = CircleArc(B, A'', A')
n = 4 (slider from 4 to 20, step 1)
l1 = Sequence(Point[c, k], k, 0, 1, 1 / n)
c' = Dilate(c, 1 - 1 / tan(α), B)
l2 = Sequence(Point[c', k], k, 0, 1, 1 / ((2 * n)))
l3 = Sequence(CircleSector[l2((2 * k)), l1(k), l1(k + 1)], k, 1, n)
d' = Dilate(d, 1 - 1 / tan(β), D)
l4 = Sequence(Point[d, k], k, 0, 1, 1 / n)
l5 = Sequence(Point[d', k], k, 0, 1, 1 / ((2 * n)))
l6 = Sequence(CircleSector[l5((2 * k)), l4(k), l4(k + 1)], k, 1, n)
l6' = Translate(l6, Vector[(t * Vector[l2(2), l1(1)])])
m = 0 (slider from 0 to 2, step 1)

Tool: 简易坐标系
请选择原点，分别输入：x最小、最大值，y最小、最大值
Input: A, a, b, c, d
Output: B, C, O, u, v

$\huge\textcolor{}{x}$

$\huge\textcolor{}{y}$

$\Large\textcolor{}{O}$

A: (0, 0)
u = Vector(A + (a - 1, 0), A + (b + 1, 0))
v = Vector(A + (0, c - 1), A + (0, d + 1))
B: A + (b + 1, 0)
C: A + (0, d + 1)
O: A