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Tetra Inequalities
Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.
Staircase
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.
Age 16 to 18 Challenge Level:
Prove that there is no arithmetic progression containing all three of $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.