Topology
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Topology is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that i
Möbius strips, which have only one surface and one edge, are a kind of object studied in topology.
A continuous transformation can turn a coffee mug into a donut. Ceramic model by Keenan Crane and Henry Segerman.
Geometry
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Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branch
A European and an Arab practicing geometry in the 15th century
Woman teaching geometry. Illustration at the beginning of a medieval translation of Euclid's Elements, c. 1310.
Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Zhoubi Suanjing 500–200 BC. The Pythagorean theorem is a consequence of the Euclidean metric.
Quintic Calabi–Yau threefold