We all know that
you can cut (or ‘dissect’) a square into 4 equal, but smaller, squares.
These are ‘self-similar’ to the original square - the same shape, but
a different size.
can do a similar thing to create a diagram with 9 smaller squares.
you do the same thing, dissecting any triangle into 4 smaller self-similar
triangles, using a similar approach ?
Problem Set 1
with the rather special triangles shown below - the 30°, 60°, 90° triangle
that is half an equilateral triangle, and the ‘half-domino’ triangle - there
are 2 nice challenges along similar lines ... :
Can you show how to dissect the first into just 3 smaller self-similar
Can you show how to dissect the second into 5 smaller self-similar
Problem Set 2
with an equilateral triangle, can you show how to dissect it into :
12 identical triangles (not necessarily equilateral)
13 equilateral triangles (not necessarily all the same size)
14 triangles of the same area (but not necessarily the same shape)
15 equilateral triangles (not necessarily all the same size)
16 equilateral triangles.
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