irrational number

Myths of maths: The golden ratio

The golden ratio has many amazing properties. But is it really a secret of nature and the epitome of beauty?

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The real numbers and Cauchy sequences

We take the real numbers for granted, but what are they really?

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Maths in a minute: The square root of 2 is irrational

Here's one of the most elegant proofs in all of maths. Rejoice in its simplicity!

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Editorial

The Plus anniversary year — A word from the editors

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A tale of two curricula: Euler's algebra text book
In the fourth and final part of our series celebrating 300 years since Leonhard Euler's birth, we let Euler speak for himself. Chris Sangwin takes us through excerpts of Euler's algebra text book and finds that modern teaching could have something to learn from Euler's methods.
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Outer space: Some benefits of irrationality
Outer space: How to beat that photocopier
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Mathematical mysteries: Transcendental meditation

Nineteenth-century German mathematician Leopold Kronecker once said

God created the integers, all the rest is the work of man.

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The origins of proof III: Proof and puzzles through the ages
For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
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  • Maths in a minute

    Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.