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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
Let m (m > 0) be a number of terms of a polynomial and n (n ≥ 0) be a power the polynomial is raised to. Let ∧ {\displaystyle \wedge } m denote a Pascal's m - simplex . Each Pascal's m - simplex is a semi-infinite object, which consists of an infinite series of its components.
The comparison t2 >= 0 is not counted as no real arithmetic takes place. In two's complement representation of the vars only the sign bit has to be checked. x=x-1 [x--] Operations: 5 t1 = r / 16 x = r y = 0 Repeat Until x < y Pixel (x, y) and all symmetric pixels are colored (8 times) y = y + 1 t1 = t1 + y t2 = t1 - x If t2 >= 0 t1 = t2 x = x - 1
(0,0) is at the top left corner of the grid, (1,1) is at the top left end of the line and (11, 5) is at the bottom right end of the line. The following conventions will be applied: the top-left is (0,0) such that pixel coordinates increase in the right and down directions (e.g. that the pixel at (7,4) is directly above the pixel at (7,5)), and
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
Pascal's theorem is the polar reciprocal and projective dual of Brianchon's theorem. It was formulated by Blaise Pascal in a note written in 1639 when he was 16 years old and published the following year as a broadside titled "Essay pour les coniques. Par B. P." [1] Pascal's theorem is a special case of the Cayley–Bacharach theorem.
In number theory, a pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from left to right or from right to left. It is named because it represents the number of 3-dimensional unit spheres which can be packed into a pentatope (a 4-dimensional tetrahedron ) of increasing ...
Consider a simple binary ("for" or "against") vote. Let m voters cast a vote of either 1 (for) or 0 (against). Each voter encrypts their choice before casting their vote. The election official takes the product of the m encrypted votes and then decrypts the result and obtains the value n, which is the sum of all the votes.