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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 ...
For instance, the traveling salesman problem, NP-hard for arbitrary sets of points in the plane, is trivial for points in convex position: the optimal tour is the convex hull. [3] Similarly, the minimum-weight triangulation of planar point sets is NP-hard for arbitrary point sets, [ 4 ] but solvable in polynomial time by dynamic programming for ...
The humerus (a.k.a. the arm bone) The arm bone is from the point of shoulder to the elbow, it is covered in heavy muscle and serves as a leverage point for the muscle of the front leg attached near the elbow. "Ideal" The humerus should be very strong and shorter than the length of the shoulder, has many points of connections for muscle.
Computing the convex hull means that a non-ambiguous and efficient representation of the required convex shape is constructed. The complexity of the corresponding algorithms is usually estimated in terms of n , the number of input points, and sometimes also in terms of h , the number of points on the convex hull.
The gömböc's shape helped to explain the body structure of some tortoises and their ability to return to an equilibrium position after being placed upside down. [ 2 ] [ 3 ] [ 4 ] Copies of the first physically constructed example of a gömböc have been donated to institutions and museums, and the largest one was presented at the World Expo ...
1. Chocolate Fondue. Think of that fondue fountain at the buffet as Willy Wonka's sacred chocolate waterfall and river. The chocolate must go untouched by human hands, or it will be ruined.
DETROIT (Reuters) -U.S. automakers Ford Motor and General Motors will donate $1 million each, along with vehicles, to U.S. President-elect Donald Trump's January inauguration, company ...
The 2024 season didn't start that poorly. They were 4-2 at the bye, though some weak opponents helped. After the bye it got ugly. Williams started to regress.