# Squaring the circle

## (UCAS interview brainteaser)

It is well known that x^2+y^2=1 is the equation of a circle with radius 1, centred at the origin. Now, suppose we let n be some positive integer. What does the graph of x^(2n)+y^(2n)=1 look like? Try thinking about how x^4+y^4=1 compares to x^2+y^2=1, before thinking about what will happen as n gets larger and larger.

**Solution** The applet below shows what happens as n increases; drag the slider to the right to see!

The shape becomes squarer and squarer as n increases.

Why did we not just look at x^n+y^n=1, do you think?

(The illustration above was made with the mathematics package Geogebra which is free to download and fun to use. Try it out for yourself!)