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Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

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Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

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The Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 15: Indexing Problems

Stage: 5 Short Challenge Level: Challenge Level:1

Consider a very big book, UltraRef, which refers in its index to every book which does not refer to itself in its index.

Does UltraRef refer to itself in its index? Be clear as to your explanation.
Did you know ... ?

Paradoxes are a fascinating feature of more advanced considerations of mathematical logic. For a century mathematicians tried to put mathematics on a totally sure logical foundation before realising that this could never be completely achieved.