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The sum of all the internal angles of a simple polygon is π(n−2) radians or 180(n–2) degrees, where n is the number of sides. The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on.
α 1 − α 2 + α 3 − ⋯ + α 2n − 1 − α 2n = 0. An equivalent way of stating the same condition is that, if the angles are partitioned into two alternating subsets, then the sum of the angles in either of the two subsets is exactly 180 degrees. [4]
The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
An n-sided regular polygon can be constructed with compass and straightedge if and only if n is either a power of 2 or the product of a power of 2 and distinct Fermat primes: in other words, if and only if n is of the form n = 2 k or n = 2 k p 1 p 2...p s, where k, s are nonnegative integers and the p i are distinct Fermat primes.
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool. Until 2015, it ran on Microsoft Windows.