A Little Noise

October 27, 2016

Square Root of a Complex Number using Compass and Straight Edge Geometry

Filed under: Technical — snoyes @ 1:09 am

Also available as an interactive applet (scrollwheel or pinch to zoom so you can adjust the axis how you want).

Descartes allowed a line segment of unit length to find roots. The rest of the construction is completed with just Euclid’s compass and straight edge.

Given: a complex number C plotted on the complex plane.
Bisect the angle formed between C, the origin O, and the positive X (real) axis.
Extend OC past O by a unit line segment to U.
Find the midpoint, M, between U and C.
Construct a half-circle centered at M through U and C.
Draw the perpendicular to UC through O to intersect the half-circle at I.
Draw a circle centered at O through I.
The circle intersects the bisector at S.
S is a square root of C.

No Comments »

No comments yet.

RSS feed for comments on this post. TrackBack URL

Leave a comment

Powered by WordPress