Just for Fun – An Elementary Scheme to Visualize the Relationship of Circle Circumference to Area | Steve Wait – May 26, 2020

From:

C=πD and A=πr²

To:

C=AD/r² and A=Cr²/D.

Constructed is a diagram depicting the sector relationship of both circumference and area of the circle (Ref. Fig. 1)

Circle data for example shown:

radius                  = 1 in
Diameter             = 2 in
Area                    = 3.14159… in²
Circumference    = 6.28319… in

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
Total of three major sector areas         = 3in²
Total of three major sector angles       = 343.774…°
Total minor sector perimeter                = .28319… in
Total minor sector area                        = .14159… in²
Total minor sector angle                      = 16.225…°

Fig. 1