The Rule of Three gained notoriety for being particularly difficult to explain: see Cocker's Arithmetick for an example of how the premier textbook in the 17th century approached the subject.
The process was continued until the doublings gave a number greater than half of the multiplier.
Beginning in the early twentieth century, mechanical calculators, such as the Marchant, automated multiplication of up to 10 digit numbers.
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In the mathematical text Zhou Bi Suan Jing, dated prior to 300 BC, and the Nine Chapters on the Mathematical Art, multiplication calculations were written out in words, although the early Chinese mathematicians employed Rod calculus involving place value addition, subtraction, multiplication and division.
Around this time Josiah Willard Gibbs and Oliver Heaviside developed vector calculus, which included separate cross product and dot products that were derived from quaternion multiplication.
Membership in co-NP is also straightforward: one can just list the prime factors of m, which the verifier can confirm to be valid by multiplication and the AKS primality test.
Shortly after 2002 the Kahun Papyrus and the RMP 2/n table revealed two aliquot part operational methods: (1) new inverse multiplication and division methods, and (2) a LCM number method written in red (RMP 38).
Algebraic expression, a mathematical expression in terms of a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational exponent)
Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function and the Fourier transform of the Gaussian function.
The miracles attested were cures of every kind (of blindness, congenital and resulting from disease, of hip and spinal disease), besides the multiplication of food for the distressed community of the Good Shepherd at Bourges in 1845.
Gibbs measure implies the Markov property (a certain kind of statistical independence); and importantly, it implies the Hammersley–Clifford theorem that the energy function can be written as a multiplication of parts, thus leading to its widespread appearance in many problems outside of physics, such as Hopfield networks, Markov networks, and Markov logic networks.
However, despite the availability of a heavy-water production facility whose output could potentially have rivalled that of Norsk Hydro at Vemork in Norway, it appears that the Japanese did not carry out neutron-multiplication studies using heavy water as a moderator at Kyoto.
The symbol * indicates multiplication and mod(A,B) denotes the modulus operator.
A more efficient multiplication method, the Schönhage–Strassen algorithm based on the Fast Fourier transform, requires O(p log p log log p) time to square a p-bit number, reducing the complexity to O(p2 log p log log p) or Õ(p2).
In this application, kilo, mega and giga are the standard S.I. prefixes indicating multiplication by 1,000 (kilo), 1,000,000 (mega), and 1,000,000,000 (giga).
Even with grade-school integer multiplication, this is only O((log n)4) time; using the multiplication algorithm with best-known asymptotic running time, the Schönhage–Strassen algorithm, we can lower this to O((log n)3(log log n)(log log log n)) time, or using soft-O notation Õ((log n)3).
Ramón Silvestre Verea Aguiar y García (Curantes, 1833 – Buenos Aires, 1899) was a Spanish journalist, engineer and writer, known as the inventor of a calculator with an internal multiplication table.
Skip counting is a mathematics technique taught as a kind of multiplication in reform mathematics textbooks such as TERC.
which, after multiplication by just tells us that the Einstein tensor of the metric defined by the tetrads vanishes.
Victorius of Aquitaine who created the Victorian system of the Cursus Paschalis and a Roman numeral multiplication table
In 1971 Strassen published another paper together with Arnold Schönhage on asymptotically-fast integer multiplication based on the fast Fourier transform; see the Schönhage–Strassen algorithm.
Scaling the output of an oscillator to a wanted volume would normally be done by multiplication, but the YM3812 avoids multiplications by operating on log-transformed signals, which reduces multiplications into computationally cheaper additions.