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The nabla is a triangular symbol resembling an inverted Greek delta: [1] or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, [2] [3] and was suggested by the encyclopedist William Robertson Smith in an 1870 letter to Peter Guthrie Tait.
Greek mathematics constitutes an important period in the history of mathematics: fundamental in respect of geometry and for the idea of formal proof. [44] Greek mathematicians also contributed to number theory , mathematical astronomy , combinatorics , mathematical physics , and, at times, approached ideas close to the integral calculus .
The OpenType font format has the feature tag "mgrk" ("Mathematical Greek") to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts. The table below shows a comparison of Greek letters rendered in TeX and HTML. The font used in the TeX rendering is an italic style.
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world; algebra started with methods of solving problems in arithmetic. The earliest ...
The graph of an involution (on the real numbers) is symmetric across the line y = x. This is due to the fact that the inverse of any general function will be its reflection over the line y = x. This can be seen by "swapping" x with y. If, in particular, the function is an involution, then its graph is its own reflection.
A simple example of the use of this formula is counting the number of reduced fractions 0 < a / b < 1, where a and b are coprime and b ≤ n. If we let f(n) be this number, then g(n) is the total number of fractions 0 < a / b < 1 with b ≤ n, where a and b are not necessarily coprime.