Square: | |

Root: |

Click & drag your mouse up and down to change the measurement, or enter a number in one of the fields and press Enter.

__Finding a square root using trigonometry__

The interactive example and equation shown above describe how we can find square roots using intersecting circles and trig functions. A key part of the equation is (n+1)/2 which is the intersecting circle radius.

__Below, some javascript code showing the equation:__

n = 5; //number to get square root of root = Math.cos(Math.asin((n-1)/(n+1)))*((n+1)/2); //2.23606797749979

__History__

I discovered this in 2008 while while studying the Vesica piscis.

Thanks to Bob Blackmon for reducing the equation further. My original equation (below) is a bit less elegant.