by Karl Scherer

It is a polygon which can be dissected into two polygons in such a way that the two parts have the same shape as the original figure,

but differ in size from each other.

**As far as I know, there is only one other polygon with this property,
namely the polygon I published in my book
"A Puzzling Journey to the Reptiles and Related
Animals". Can you find this polygon? **

**When you are about to give up your search, click
here for the solution and proof (for n<7).
**

**Dissect a regular triangle into three similar parts (i.e. the parts
should have the same shape, but can differ by size). **

** a. Solve the problem such that the three parts have all the same
size.
b. Solve the problem such that exactly two of the three parts have
the same size.
c. Solve the problem such that the three parts have all different
size. **

**It turns out that problems a. and c. have been solved thousands of years
ago by the greek scientists,
but part b stayed unsolved until I found the solution as part of my work
on the book "A
Puzzling Journey to the Reptiles
and Related Animals".**

**Try to find answers to all three parts before you click here for the solutions.
**

**Tile a regular hexagon into four congruent shapes.
There are two solutions (apart from rotations and reflections). Can you
find them?
Click here to see the solutions.
**

**Tile a regular hexagon into seven similar shapes (i.e. same shapes,
but sizes may vary).
There are four solutions (apart from rotations and reflections). Can you
find them?**

** Click here to see the solutions.
**