Donut - Fundamental Polygon of a Torus #maths #topology #torus

🌟 We can define the torus T^2 ("donut") as a quotient space of the unit square by identifying points as shown in the video:

▶ (0, y) ~ (1, y) to obtain a cylinder
(see 0:01 in video)

and

▶ (x, 0) ~ (x, 1) which is achieved by stretching the obtained cylinder and identifying the points on its top and bottom
(see 0:04 in video)

Therefore T^2 = I x I / ~(left-right) / ~(top-bottom) where I := [0,1] ⊆ R. If you're unsure about the notion of "/", see "quotient space" in topology.

🌟 If you're interested in this topic, you may want to search for the following keywords:
- equivalence relation
- quotient space (topology), quotient map
- fundamental polygon

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