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

### The Square Hole

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

### An Introduction to Irrational Numbers

Tim Rowland introduces irrational numbers

# Equal Equilateral Triangles

##### Age 14 to 16 Challenge Level:
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Click on the green or yellow triangles to get a copy.
Drag the triangle by its interior to the required position and drag any vertex to rotate it.
• Can you make a regular hexagon using only yellow triangles ?

• Can you make a regular hexagon using only green triangles ?

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

Did that tell you something about yellow and green triangles, about how they relate to each other ?

• Can you make an equilateral triangle from yellow triangles ?
• Can you make an equilateral triangle from green triangles ?
• Can you make an equilateral triangle from yellow triangles that is the same size as an equilateral triangle made from green triangles ?

Hold down SHIFT and click here to listen to the audio file . The audio will then start in a new window.

Also, if you wish, follow the 'Hint' tab at the top of this screen for more help.

And when you've got inside this problem and started to feel your way around, please do take a look at Impossible Triangles? - it's the perfect follow on. There's even a video to watch to make getting started easy.