ELI5: hyperbolic geometry
// explanation
What is hyperbolic geometry?
Hyperbolic geometry is a type of math that describes shapes on a curved surface that bends away from you, kind of like the inside of a bowl [1]. Unlike the flat geometry you learn in school, hyperbolic geometry has different rules for how shapes work [1].
Why is it different from regular geometry?
In regular flat geometry, the angles in a triangle always add up to 180 degrees [4]. But in hyperbolic geometry, the angles in a triangle add up to less than 180 degrees because the surface is curved inward [4].
What does it look like?
Hyperbolic geometry is hard to picture because we live in mostly flat space, but imagine living on the inside of a never-ending bowl where space gets bigger and bigger as you move outward [2]. Things that are far away look really small, kind of like how perspective works in a painting [5].
Where do we use it?
Hyperbolic geometry shows up in some cool patterns and designs, and mathematicians use it to understand the shape of space itself in the universe [3].
// sources
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.
Dec 5, 2014 ... Hyperbolic geometry is a bit harder to visualise intuitively, since flat space and spherical space are easy to relate too.
Nevertheless with the passage of time it has become more and more apparent that the negatively curved geometries, of which hyperbolic non-Euclidean geometry is ...
In hyperbolic geometry, the sum of angles of a triangle is less than 180 degrees, and triangles with the same angles have the same areas.
Dec 21, 2016 ... A hyperbolic polygon is a region of the hyperbolic plane whose boundary is decomposed into finitely many generalized line segments (recall that ...
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Video by Mathematical Association of America
