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The branch of mathematics concerned with properties of spatial measurements . This includes distance, shape, size, and even theoretical dimensional spaces higher than 3D. A mathematician who specializes in geometry is known as a geometer.

Euclidean geometry, the study of flat surfaces and spatial measurements surrounding them, began in Ancient Greece with the likes of Pythagoras, Archimedes, and Euclid. Euclid developed five basic postulates, the fifth being the famed "Parallel Postulate".

The parallel postulate is not provable as a theorem. This led to a lot of geometry branches that ignore the postulate entirely. The most famous of these non-Euclidean geometries is hyperbolic geometry.

There are other branches of geometry that are still in their infancy. One of these is fractal geometry, the branch of geometry concerned with fractals, shapes whose Hausdorff dimension is much greater than their topological dimension.

As you can see, geometry is an extremely broad branch of mathematics, with many different branches.

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