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Ladder and Cube

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 18
Challenge 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.