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(more unsolved problems in mathematics) In mathematics , a self-avoiding walk ( SAW ) is a sequence of moves on a lattice (a lattice path ) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path .
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, [1] to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. It is possible, using pieces that are Borel sets, but not with pieces cut by Jordan curves.
This problem has straightforward solutions in a sufficiently powerful OO programming system. Essentially, the circle–ellipse problem is one of synchronizing two representations of type: the de facto type based on the properties of the object, and the formal type associated with the object by the object system. If these two pieces of ...
One common type of approach is claiming to have solved a classical problem that has been proven to be mathematically unsolvable. Common examples of this include the following constructions in Euclidean geometry—using only a compass and straightedge: Squaring the circle: Given any circle drawing a square having the same area.
The oblique exercises below are the best in the game and perfect for all strength levels. Mix one or two moves into your core routine or full-body sessions, or string them together for a spicy ...
The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution. Prince Rupert's cube is named after Prince Rupert of the Rhine , who asked whether a cube could be passed through a hole made in another cube of the same size without splitting the cube into two pieces.
The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).
The minimum number of transversals of a Latin square is also an open problem. H. J. Ryser conjectured (Oberwolfach, 1967) that every Latin square of odd order has one. Closely related is the conjecture, attributed to Richard Brualdi, that every Latin square of order n has a partial transversal of order at least n − 1.