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:

To four places of decimals $\sqrt{56} = 7.4833\;\mbox{ and }\; \sqrt{58} = 7.6158$

If $\sqrt{56} < \frac{p}{q} < \sqrt{58}$, then $56q^2 < p^2< 58q^2$

Try different values of $q$, and remember $p$ is a whole number.