Difficult Dissections
by Karl Scherer

1. A Difficult Dissection into Two Parts
A (non-isosceles) right triangle has the following extraordinary property:
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).


2. Dissect A Regular Triangle Into Three Similar Parts

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.


3. Dissect A Regular Hexagon Into Four Congruent Parts

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.


4. Dissect A Regular Hexagon Into Seven Similar Parts

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.




Back to home page