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Equate is a board game made by Conceptual Math Media where players score points by forming equations on a 19x19 game board. Equations appear across and down in a crossword fashion and must be mathematically correct. Because of its characteristics, the game is often described as a Scrabble with math. [1] [2]
Number Munchers is the first educational game in the Munchers series. Designed to teach basic math skills, it was popular among American school children in the 1980s and 1990s and was the recipient of several awards. [2] An updated 3D version, Math Munchers Deluxe, was released in 1995. [3]
Multiplication of 2 + i (blue triangle) and 3 + i (red triangle). The red triangle is rotated to match the vertex of the blue one (the adding of both angles in the terms φ 1 +φ 2 in the equation) and stretched by the length of the hypotenuse of the blue triangle (the multiplication of both radiuses, as per term r 1 r 2 in the equation).
The constants R mod N and R 3 mod N can be generated as REDC(R 2 mod N) and as REDC((R 2 mod N)(R 2 mod N)). The fundamental operation is to compute REDC of a product. When standalone REDC is needed, it can be computed as REDC of a product with 1 mod N. The only place where a direct reduction modulo N is necessary is in the precomputation of R ...
The game Equals was a board game similar to Scrabble, but instead of tiles with letters combined to form words, it used tiles with numbers and basic arithmetic operations to form equations. [ 1 ] The game was sold originally as Zahlenjux by Pelikan in Germany, [ 2 ] and in Canada was licensed by Waddingtons .
The latter is impossible because a is a real number and the first equation would imply that a 2 = −1. Therefore, a = 0 and b 2 + c 2 + d 2 = 1. In other words: A quaternion squares to −1 if and only if it is a vector quaternion with norm 1. By definition, the set of all such vectors forms the unit sphere.
Addition and multiplication are both associative, which means that (+) + = + (+) and () = for every real numbers a, b and c, and that parentheses may be omitted in both cases. Multiplication is distributive over addition, which means that a ( b + c ) = a b + a c {\displaystyle a(b+c)=ab+ac} for every real numbers a , b and c .
Karatsuba's basic step works for any base B and any m, but the recursive algorithm is most efficient when m is equal to n/2, rounded up. In particular, if n is 2 k , for some integer k , and the recursion stops only when n is 1, then the number of single-digit multiplications is 3 k , which is n c where c = log 2 3.