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Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, [2] the Pythagoreans (in particular Philolaus and Archytas) [3] of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, [4] particularly the ratios of small integers.
The Blue Book is a compact disc standard that defines the Enhanced Music CD format, which combines audio tracks and data tracks on the same disc. E-CD/CD+/CD Extra ( Enhanced ) [ 21 ] – a standard jointly developed and published by Microsoft , Philips and Sony
Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. [2] [3]
Cutting the pants along the seams, one gets two right-angled hyperbolic hexagons which have three alternate sides of matching lengths. The following lemma can be proven with elementary hyperbolic geometry. [4] If two right-angled hyperbolic hexagons each have three alternate sides of matching lengths, then they are isometric to each other.
Download as PDF; Printable version; ... out of 2 total. M. ... Pages in category "Mathematics of music" The following 14 pages are in this category, out of 14 total.
For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations. It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence A180632 in the OEIS). The first four smallest ...
Three vinyl records of different formats, from left to right: a 12 inch LP, a 10 inch LP, a 7 inch single. A phonograph record (also known as a gramophone record, especially in British English) or a vinyl record (for later varieties only) is an analog sound storage medium in the form of a flat disc with an inscribed, modulated spiral groove.
It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius. Disc: the region of the plane bounded by a circle. In strict mathematical usage, a circle is only the boundary of the disc (or disk), while in everyday use the term "circle" may also refer to a disc.