### Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90Â°, (45+x)Â° and (45-x)Â° in a triangle?

### After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

### Small Steps

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

# Squareness

##### Age 16 to 18Challenge Level

(1) Consider each quadrant separately or use a symmetry argument.

(2) Write $2^{1/n} = 1 + \delta$ and use the Binomial Theorem.

(3) Consider the symmetry of the graph and the point at which it cuts the line $y=x$.

(4) Use the result of (3) and a symmetry argument.

(5) Consider each quadrant separately.