Constructing the Square Root of a Positive Integer Geometrically

integer n

2

This Demonstration finds the square root of a positive integer

n

geometrically. From a point on a vertical line, draw a perpendicular segment of length

(n-1)/2

and then a circle of radius

(n+1)/2

centered at the endpoint of this segment. The intersection of the vertical line and the circle is at the distance

n

from the original point.