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Tetra Inequalities

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?


Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?

Proof Sorter - the Square Root of 2 Is Irrational

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

Be Reasonable

Age 16 to 18
Challenge Level

Prove that there is no arithmetic progression containing all three of $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$.