### Equal Equilateral Triangles

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

### 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

# Rationals Between

##### Stage: 4 Challenge Level:

I am searching for fractions with values between $\sqrt{56}$ and $\sqrt{58}$. I'm told there are an infinite number of possibilities...

Find some fractions with small denominators, say less than $10$ or $20$.
Have you found any denominators which won't yield a fraction between $\sqrt{56}$ and $\sqrt{58}$?

Send us any examples you find of denominators which don't work, and a justification that all other denominators will work!