Squaring the circle

Squaring the circle is a problem in geometry 

first proposed in Greek mathematics. It is the challenge of 

constructing a square with the area of a given circle 

by using only a finite number of steps 

with a compass and straightedge. 

Area of contained smaller lune

.785 - .5 = .285

Area of Uncontained Larger Lune

.785 - .285 = .5

Area of smaller circle 

.785 + .785 = 1.57

a square of Area of  1.57 has

side length = Square root of 1.57

= 1.25299640861

1.57 + 1.57 = 3.14

Area of the Larger Circle

.5 X 4 = 2.00

.285 X 4 = 1.14

Total area =  3.14

Square root of 3.14 = 1.7720

Smaller circle

the small circle dimensions

Radius: square root of two 

                   divided by two

Diameter: square root of two

Cord Length: One

Area of Half the smaller circle

.785

Area of the Smaller circle

1.57

Larger Circle

Radius: One

Diameter: two

Cord Length: square root of two

Quarter of the larger circle

Area of Quarter of the Larger Circle

.785

Area of Half the Larger Circle

1.57

Area of the Larger Circle

3.14