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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If a {\displaystyle a} is an integer , the answer is a 2 , {\displaystyle a^{2},} but the precise – or even asymptotic – amount of unfilled space for an arbitrary ...
Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. The optimal packing of 10 squares in a square
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 in order to maximize the minimal separation, d n, between points. [1] To convert between these two formulations of the problem ...
Comparison of 1 square metre with some Imperial and metric units of area. The square metre (international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m 2. [1]
Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the matrix A. The approximate solution is realized as an exact solution to A x = b', where b' is the projection of b onto the column space of A. The best ...
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Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.