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Degree Ceremony
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
Small Steps
Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Age 16 to 18
Challenge Level
(1) Consider each quadrant separately or use a symmetry argument.
(2) Write $2^{1/n} = 1 + \delta$ and use the Binomial Theorem.
(3) Consider the symmetry of the graph and the point at which it cuts the line $y=x$.
(4) Use the result of (3) and a symmetry argument.
(5) Consider each quadrant separately.
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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.