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Equation Attack

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

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Root Hunter

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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Archimedes Numerical Roots

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Two Trees

Age 16 to 18 Challenge Level:

Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?