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A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Growing

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

### Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

# Back Fitter

##### Age 14 to 18Challenge Level
Start by looking for data which can be matched to straightforward functions like a straight line, or a quadratic.

Which data sets oscillate? What functions do you know which oscillate?

If you are unfamiliar with the graphs of $y=a^x$ and $y=a^{-x}$ for different values of the constant $a$, try plotting them using graphing software or a graphical calculator.