Article
What is a square?
If a shape has equal sides with 90 degree angles between them then it's a square, right? Well, not quite...
Content about “ curvature
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The unreasonable relationship between mathematics and physics
Can physics do for maths what maths has done for physics?
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If our Universe is expanding, then what is it expanding into?
Since he Universe is all there is, there's nothing for it to expand into. So what does "expansion" mean?
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Kissing the curve – manifolds in many dimensions
Following on from our previous article about curvature of lines and surfaces, we now move up to curvature of their higher dimensional equivalent – manifolds.
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Kissing the curve
Curves bring great beauty to our world. But how curvy is a curve?
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Hidden dimensions
That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. Plus met up with mathematician Shing-Tung Yau to find out more.
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Mathematical mysteries: Strange Geometries
The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.
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In space, do all roads lead to home?
Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.