The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers...

relate logarithms to one another. The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two...

known as the mantissa. Tables of common logarithms typically included only the mantissas; the integer part of the logarithm, known as the characteristic...

Representations of e El Gamal discrete log cryptosystem Harmonic series History of logarithms Hyperbolic sector Iterated logarithm Otis King Law of the iterated...

algorithms called logarithms that economized arithmetic by rendering multiplications into additions. So F was first known as the hyperbolic logarithm. After Euler...

taken to mean the "logarithms" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm): N a p L o g ( x...

use of logarithms avoided laborious and error-prone paper-and-pencil multiplications and divisions. Because logarithms were so useful, tables of base-10...

of logarithms, high accuracy numerical calculations involving multiplication, division and root extraction were laborious and error prone. Logarithms...

already compiled a table of what in fact were effectively natural logarithms in 1619. It has been said that Speidell's logarithms were to the base e, but...

function to the transcendental function ex. To accommodate the case of negative logarithms and the corresponding negative hyperbolic angles, different hyperbolic...

studied how to compute logarithms by geometrical methods and calculated a quantity that, in retrospect, is the base-10 logarithm of e, but he did not recognize...

Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to...

logarithms (also known as Jacobi logarithms), but uses a system of indices original to Ludgate. Ludgate's algorithm compresses the multiplication of two...

logarithms, which follows these steps: scale down, take logarithms, add, take inverse logarithm, scale up. It is no surprise that the originators of logarithms...

property characterizes logarithms, and it was mathematical fashion to call such a function A ( x ) {\displaystyle A(x)} a logarithm. In particular when we...

changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honor. The...

values in the positive reals. For example, since the logarithm of a product is the sum of the logarithms of the factors, we have ( log ⁡ u v ) ′ = ( log ⁡ u...

for powers and logarithms for positive real numbers will fail for complex numbers, no matter how complex powers and complex logarithms are defined as...

more. As of November 2024[update], the fastest supercomputer is El Capitan. Starting with known special cases, the calculation of logarithms and trigonometric...

other than James I, that Hume applauds is John Napier of Merchiston, the inventor of logarithms. However Napier, Newton and James I are criticised for...

The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical...

intervals. The representation of musical intervals by logarithms is almost as old as logarithms themselves. Logarithms had been invented by Lord Napier...

that used discrete logarithms to calculate products of integers without approximation. The Model 366 is notable for its table of numbers, mapping the...

these areas can fill the place of the given logarithms … ). [In other words, the areas are proportional to the logarithms.] See also: Enrique A. González-Velasco...

fully understand complex logarithms. Euler also suggested that complex logarithms can have infinitely many values. The view of complex numbers as points...

Hindu mathematical traditions as part of the biographical memoir on John Napier and the history of logarithms. The biography project appears to have...

multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the logarithms of those numbers. While producing...

Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. Nearly fifteen years earlier, Alexander...

The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Due...

"Madhava of Sangamagramma". MacTutor History of Mathematics Archive. Pearce, Ian G. (2002). "Madhava of Sangamagramma". MacTutor History of Mathematics...