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In the game of Vish (short for vicious circle), players compete to find circularity in dictionary definitions. [1] Irish mathematician and physicist, John Lighton Synge, invented the multi-player, refereed game to emphasize the circular reasoning implicit in the defining process of any standard dictionary.
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]
The amount of bending is approximately 1 / 28 unit (1.245364267°), which is difficult to see on the diagram of the puzzle, and was illustrated as a graphic. Note the grid point where the red and blue triangles in the lower image meet (5 squares to the right and two units up from the lower left corner of the combined figure), and ...
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The open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. The unit circle is the Cayley absolute that determines a metric on the disk through use of cross-ratio in the style of the Cayley–Klein metric.
Orthogonal polynomials on the unit circle. Part 1. Classical theory. American Mathematical Society Colloquium Publications. Vol. 54. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-3446-6. MR 2105088. {}: CS1 maint: date and year ; Simon, Barry (2005). Orthogonal polynomials on the unit circle. Part 2. Spectral theory. American ...
Moreover, since the unit circle is a closed subset of the complex plane, the circle group is a closed subgroup of (itself regarded as a topological group). One can say even more. The circle is a 1-dimensional real manifold, and multiplication and inversion are real-analytic maps on the circle.
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