From C = π D and A = π r2 to C = A D / r2 and A = C r2 / D.
Constructed is a diagram depicting the sector relationship of both Circumference and Area of a Circle (Ref. Fig. 1)
Circle data for example shown:
radius = 1in
Diameter = 2in = 2 x 1in = 2 r
Area = 3.14159+in² = 3.14159+ x (1in x 1in) = π r²
Circumference = 6.28319+in = 3.14159+ x 2in = π D
Three major sectors, each having both a circumferential perimeter equal to the Diameter, and an area equal to the radius squared. Each represents 2 radians.
One minor sector, bearing both a circumferential perimeter equal to the total Circumference less the sum of the three major sectors, and an area equal to the total Area less the sum of the same. Here, representing .28319+ radians.
Sector data for example shown:
total of three major sector perimeters = 6in = 3D
total of three major sector areas = 3in² = 3 r²
total of three major sector angles = 343.774+° = 3 x 114.591+°
total minor sector perimeter = .28319+in = π D – 3 D
total minor sector area = .14159+in² = π r² – 3 r²
total minor sector angle = 16.225+° = 360°- 343.774+°
Fig. 1
