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I think it shows well enough how the mug and the torus are topologically equivalent, and it just requires a little bit of thought to figure that the bottom of the cup is rising to the top in order to make the overall shape convex for a smooth transition, and it seems that once the average person realizes this the whole concept of topological ...
The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup. [ 1 ] When the cup is filled, liquid rises through the second pipe up to the chamber at the top of the central column, following Pascal's principle of communicating vessels .
Dizzy Cocktail glass, a glass with a wide, shallow bowl, comparable to a normal cocktail glass but without the stem; Collins glass, for a tall mixed drink [2]; Highball glass, for mixed drinks [3]
This illustrates that a coffee mug and a donut are homeomorphic. In mathematics and more specifically in topology , a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré ), [ 2 ] [ 3 ] also called topological isomorphism , or bicontinuous function , is a bijective and continuous function between topological spaces ...
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Poloidal direction (red arrow) and toroidal direction (blue arrow) A torus of revolution in 3-space can be parametrized as: [2] (,) = (+ ) (,) = (+ ) (,) = using angular coordinates θ, φ ∈ [0, 2π), representing rotation around the tube and rotation around the torus's axis of revolution, respectively, where the major radius R is the distance from the center of the tube to ...