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Simpson's rule is a method for approximating definite integrals based on quadratic interpolation. Learn about Simpson's 1/3 rule, Simpson's 3/8 rule, composite Simpson's rule, and their derivations, errors, and applications.
A well-known ancient Egyptian mathematical text from the Second Intermediate Period, copied by the scribe Ahmes in 1550 BC. It contains problems and tables on arithmetic, algebra, geometry, and fractions, as well as a historical note on its origin.
Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. It represents hyperoperations such as tetration, pentation, etc., which are iterated versions of addition, multiplication, and exponentiation.
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]
A Farey sequence of order n is a list of fractions with denominators less than or equal to n, arranged in increasing order. Learn about the properties, examples, and applications of Farey sequences, also known as Farey series.
A continued fraction is an expression obtained by representing a number as the sum of its integer part and the reciprocal of another number, then repeating the process. Learn how to find the continued fraction representation of rational and irrational numbers, and see some examples of famous numbers and their continued fractions.
It is now clear that if the warden answers B to A ( 1 / 2 of all cases), then 1 / 3 of the time C is pardoned and A will still be executed (case 4), and only 1 / 6 of the time A is pardoned (case 1). Hence C's chances are ( 1 / 3 )/( 1 / 2 ) = 2 / 3 and A's are ( 1 / 6 )/( 1 / 2 ) = 1 / ...
The Riemann hypothesis is a conjecture about the zeros of the Riemann zeta function, a complex function that relates to prime numbers. It states that all non-trivial zeros have real part 1/2, and implies many results about the distribution of primes.