
A while ago John Diamantopoulos sent us some beautiful visual proofs of Pythagoras' theorem. He has now been in touch again with visual proofs of two well-known algebraic identities. The first one is
You can see that this is true in John's Geogebra applet below: the square with side length
The second identity is
To see why this is true geometrically we need to use cubes, rather than squares. Again, it turns out that a cube with side length
In the Geogebra applet below, use the slider on the left to adjust the ratio between
About this article

John C. D. Diamantopoulos is a Professor in the Department of Mathematics and Computer Science at Northeastern State University in Tahlequah, Oklahoma. His mathematical interests include ordinary differential equations, mathematics education and the history of mathematics. Diamantopoulos is also very active in his church, volunteering on computer productions/presentations and any area that needs attention.
Comments
Mathematics
Excellent efforts
Easy to understand!
Easy to understand!