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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

Repetitiously

Can you express every recurring decimal as a fraction?

Equal Equilateral Triangles

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

The Square Hole

Age 14 to 16
Challenge Level


If you take the side length of the yellow equilateral triangle as the unit for length, what would be the size of the hole ?

Alternatively, if the area of the yellow equilateral triangle is taken as the unit for area, what size is the hole then ?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.