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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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Religion
Hear from blasphemes, sceptics and free-thinkers in this ‘tour of medieval unbelief’
52 minutes
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Ecology and environmental sciences
The ancient Hawaiian myth that sparked a modern ecological breakthrough
10 minutes
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Art
The irreverent duo who thumbed their noses at the Soviet Union and the US art world
11 minutes
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Computing and artificial intelligence
A scientist’s poor eyesight helped fuel a revolution in computer ‘vision’
9 minutes
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Ageing and death
Demystifying death – a palliative care specialist’s practical guide to life’s end
4 minutes
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Future of technology
Is this the future of space travel? Take a luxury ‘cruise’ across the solar system
6 minutes
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Metaphysics
Why mathematical truths exist with or without minds to consider them
8 minutes
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Fairness and equality
A tragicomic account of how the Los Angeles Police Department blew up a city block
19 minutes
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Stories and literature
A French Creole folktale nearly lost to time is given new, gorgeously animated life
6 minutes