Information om | Engelska ordet FOUR-SQUARE

Exempel på hur man kan använda FOUR-SQUARE i en mening

• This question later became known as Bachet's conjecture, after the 1621 translation of Diophantus by Claude Gaspard Bachet de Méziriac, and it was solved by Joseph-Louis Lagrange in his four-square theorem in 1770, the same year Waring made his conjecture.
• Quaternions derive from the four-square identity, which can be written as the product of two inner products of 4-dimensional vectors, yielding again an inner product of 4-dimensional vectors:.
• 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.
• Analogous identities are Euler's four-square related to quaternions, and Degen's eight-square derived from the octonions which has connections to Bott periodicity.
• The use of digraphs makes the four-square technique less susceptible to frequency analysis attacks, as the analysis must be done on 676 possible digraphs rather than just 26 for monographic substitution.
• The Cherokee did not, unlike The Siege of Belgrade, attempt to add any "exotic" music for the Cherokee – their "War March" is disappointingly four-square and tonal, but the "War Whoop" is an exciting number.
• More recent views are from Arthur Hutchings, Nicholas Temperley and Jeremy Dibble, seeing Dykes's work in from the baseline of Nahum Tate and Nicholas Brady's New Version of the Psalms published at the end of the 17th century, and its four-square long metre tunes.
• Immediately after the discovery of quaternions, before the end of 1843, Graves successfully extended to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".

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