演示

k = 1 (slider from 0 to 1)
A = (-0.6608, 0.3212)
r = 1 (slider from 1 to 5)
B: A + (((2 * π) * r), 0)
C = Point(Segment[A, B], k)
O: C + (0, r)
f = Segment(A, C)
C' = Rotate(C, ((-f)) / r, O)
c = CircleArc(O, C, C')
d = If(C ≟ A, Circle[O, r])
A1: 0.1
A2: 0.2
A3 = 0.30000000000000004
A4 = 0.4000000000000001
A5 = 0.5000000000000001
A6 = 0.6000000000000001
A7 = 0.7000000000000001
A8 = 0.8
A9 = 0.9
B1, C1, D1 = 圆周展开(A + (0, A1), r - A1, k)
B2, C2, D2 = 圆周展开(A + (0, A2), r - A2, k)
B3, C3, D3 = 圆周展开(A + (0, A3), r - A3, k)
B4, C4, D4 = 圆周展开(A + (0, A4), r - A4, k)
B5, C5, D5 = 圆周展开(A + (0, A5), r - A5, k)
B6, C6, D6 = 圆周展开(A + (0, A6), r - A6, k)
B7, C7, D7 = 圆周展开(A + (0, A7), r - A7, k)
B8, C8, D8 = 圆周展开(A + (0, A8), r - A8, k)
B9, C9, D9 = 圆周展开(A + (0, A9), r - A9, k)
D: A + (0, r)
text2 = LaTeX("r")
h = Segment(A, D)
g = PolyLine(A, B, D, A)
text1 = LaTeX("2 π r")
text3 = LaTeX("S= π r^2")
n = 2 (slider from 0 to 30, 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

Tool: 圆周展开
起点，半径，路径值
Input: A, r, k
Output: c, d, f

B: A + (((2 * π) * r), 0)
C = Point(Segment[A, B], k)
O: C + (0, r)
f = Segment(A, C)
C' = Rotate(C, ((-f)) / r, O)
c = CircleArc(O, C, C')
d = If(C ≟ A, Circle[O, r])