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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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Knowledge
Why it takes more than a lifetime to truly understand a single meadow
11 minutes
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Physics
Groundbreaking visualisations show how the world of the nucleus gives rise to our own
10 minutes
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War and peace
‘She is living on in many hearts’ – Otto Frank on the legacy of his daughter’s diary
12 minutes
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Art
Why Diego Velázquez needed a lifetime to paint his enigmatic masterpiece
31 minutes
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Earth science and climate
There’s a ‘climate bomb’ ticking beneath the Arctic ice. How can we prepare?
8 minutes
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Political philosophy
The radical activist couple who fought for social change in the courtroom
21 minutes
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Physics
To change the way you see the Moon, view it from the Sun’s perspective
5 minutes
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Human rights and justice
When a burial for slave trade victims is unearthed, a small island faces a reckoning
29 minutes
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Ecology and environmental sciences
GPS tracking reveals stunning insights into the patterns of migratory birds
6 minutes