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In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. [1] Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13). A primitive Pythagorean triple is one in which a, b and c are coprime (the greatest common divisor of a ...
Square number. Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [ 1 ] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.
Elegy Written in a Country Churchyard is a poem by Thomas Gray, completed in 1750 and first published in 1751. [1] The poem's origins are unknown, but it was partly inspired by Gray's thoughts following the death of the poet Richard West in 1742. Originally titled Stanzas Wrote in a Country Church-Yard, the poem was completed when Gray was ...
Goldbach's conjecture is used when studying computation complexity. [36] The connection is made through the Busy Beaver function, where BB (n) is the maximum number of steps taken by any n state Turing machine that halts. There is a 27 state Turing machine that halts if and only if Goldbach's conjecture is false.
A word square is a type of acrostic. It consists of a set of words written out in a square grid, such that the same words can be read both horizontally and vertically. The number of words, which is equal to the number of letters in each word, is known as the "order" of the square. For example, this is an order 5 square:
Horatio Walpole, 4th Earl of Orford (/ ˈ w ɔː l p oʊ l /; 24 September 1717 – 2 March 1797), better known as Horace Walpole, was an English writer, art historian, man of letters, antiquarian, and Whig politician. [1] He had Strawberry Hill House built in Twickenham, southwest London, reviving the Gothic style some decades before his ...
Over a ternary alphabet, a square-free word of length more than 13 contains all the square-free two-letter combinations. This can be proved by constructing a square-free word without the two-letter combination ab. As a result, bcba cbca cbaca is the longest square-free word without the combination ab and its length is equal to 13.
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative integer squares. [1] That is, the squares form an additive basis of order four.