Search results
Results from the WOW.Com Content Network
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).
The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.
2.3 Trigonometric, inverse trigonometric, hyperbolic, ... 7.4 Reciprocal of tetrahedral numbers. 7.5 Exponential and logarithms. 8 See also. 9 Notes. 10 References.
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum , as Leonhard Euler proved in 1737. Like rational numbers , the reciprocals of primes have repeating decimal representations.
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
P ' is the inverse of P with respect to the circle. To invert a number in arithmetic usually means to take its reciprocal. A closely related idea in geometry is that of "inverting" a point. In the plane, the inverse of a point P with respect to a reference circle (Ø) with center O and radius r is a point P ', lying on the ray from O through P ...
Inverse proportionality with product x y = 1 . Two variables are inversely proportional (also called varying inversely , in inverse variation , in inverse proportion ) [ 2 ] if each of the variables is directly proportional to the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. [ 3 ]
The magenta line shows that the harmonic mean of 6 and −2 is −6. The red line shows that the harmonic mean of a number and its negative is undefined as the line does not intersect the z axis. For the special case of just two numbers, and , the harmonic mean can be written as: [4]