# Dissecting a Regular Triangle into Three Similar Tiles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Two figures are called similar if they have the same shape; they may have different sizes.

[more]
Contributed by: Karl Scherer (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Dissecting a regular triangle into three similar polygons, two of them of the same size, looks quite impossible at first glance.

Hence it is no wonder that this problem was unsolved until 1987, when the author of this Demonstration stumbled upon it as part of working on his book *A Puzzling Journey To The Reptiles And Related Animals* on irregular rep-tiles. The surprising solution can also be found in his Zilllions game 'Isolattice'. The solution became widely known when Martin Gardner published it.

## Permanent Citation

"Dissecting a Regular Triangle into Three Similar Tiles"

http://demonstrations.wolfram.com/DissectingARegularTriangleIntoThreeSimilarTiles/

Wolfram Demonstrations Project

Published: March 7 2011