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A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments.Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation.
In 1999, a theorem due to Haga provided constructions used to divide the side of a square into rational fractions. [19] [20] In late 2001 and early 2002, Britney Gallivan proved the minimum length of paper necessary to fold it in half a certain number of times and folded a 4,000-foot-long (1,200 m) piece of toilet paper twelve times. [21] [22]
The diagonal displays an approximation of the square root of 2 in four sexagesimal figures, 1 24 51 10, which is good to about six decimal digits. 1 + 24/60 + 51/60 2 + 10/60 3 = 1.41421296... The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888...
A table of constants that includes the same approximation of the square root of 2 as YBC 7289 is the tablet YBC 7243. The constant appears on line 10 of the table along with the inscription, "the diagonal of a square". [2] [4] [5] The mathematical significance of this tablet was first recognized by Otto E. Neugebauer and Abraham Sachs in 1945.
The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
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