What’s non-Euclidean geometry?

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I never got beyond calculus in school, and I’ve heard this term thrown around by smart math and science people bit have no clue what it means or why it’s special.

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Anonymous 0 Comments

Geometry in space that is not uniformly distributed.

Imagine a 3D graph with two diagonal parallel lines. Both lines increment the same amount of Y for every X. Let’s say that Z is constant but different from one another, i.e.; one line is further away from the other but they have the same angle.

Keep that in mind.

Now, if we imagine the grid of such a graph, it would be composed of cubes.

In Euclidean space we treat all these cubes as uniform; they all share the same width, height and depth. But what if they didn’t?

In non-Euclidian space those cubes can have different dimensions. Some could have more width than others for example. If the width of the cubes increases with Z, the line in the back would appear (from the perspective of the line in the front) to have a steeper angle. It has more “X” per X in the front which means that it moves more in the Y direction. The parallel lines appear to cross. However both lines still increase the same amount of Y per X!

If we would look from the line in the back to the one in the front it would appear to decrease in angle. It has less “X” per X in the back which means that it moves less in the Y direction.

Space itself is non-euclidian in nature. Gravitational lensing is a phenomena that describes how light bends around large masses due to them distorting spacetime, i.e.; mass influences the size of the “grid cubes” in space.

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