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First discovered by the Italian mathematician Giuseppe Peano in 1890, a space-filling curve can theoretically expand endlessly without its path ever crossing itself to fill an infinite space. In a computer display, space-filling curves are limited by the number of pixels on a screen, but watching these fractal constructions extend isn’t just hypnotic – it’s also a helpful (if somewhat imperfect) demonstration of the enigmatic concept of infinity. To learn more about the mathematics of space-filling curves, watch Hilbert’s Curve, and the Usefulness of Infinite Results in a Finite World, also by 3Blue1Brown.
Video by 3Blue1Brown
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Biology
An elegy for a dying microbe explores what we really mean by ‘death’
9 minutes
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Art
Creating art that was aware of itself – and the viewer – made Manet the first modernist
15 minutes
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Biotechnology
It’s our responsibility to engineer corals that can weather the world we’ve created
11 minutes
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Physics
Imagining spacetime as a visible grid is an extraordinary journey into the unseen
12 minutes
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War and peace
A century later, can poetry help us make sense of the First World War’s horrors?
9 minutes
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Language and linguistics
The little Peruvian guide to public speaking that conjures up a grandiose world
7 minutes
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Engineering
For one of nature’s great builders, finding a mate means weaving the perfect nest
4 minutes
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The ancient world
Archeological discoveries animate the life of the warrior queen who took on Rome
6 minutes
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Biography and memoir
Preserving memories of a Japanese internment camp, and the land where it stood
8 minutes