What fractions can you find between the square roots of 65 and 67?
If the yellow equilateral triangle is taken as the unit for area,
what size is the hole ?
Tim Rowland introduces irrational numbers
The screen shot on the
Hints page shows some solution
When we looked at the solutions sent in,
some people had started by putting triangles together until they
could make a hexagon, others started with a hexagon and looked for
ways it might split up into the two types of triangle.
This is great reasoning, but how do we
know that replacing each equilateral space with three green
triangles is the only way to build up to an equilateral triangle
?We hope you enjoy the brain-stretching this kind of reasoning
involves.Be encouraged, students a lot older than Stage 4 still
wrestle with this sort of thinking.