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🔗 Mathematics

Sexagesimal (also known as base 60 or sexagenary) is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.

The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6.

In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. For example, 10 means the number ten and 60 means the number sixty.

🔗 Mathematics

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.

Under the definition as repeated exponentiation, the notation ${\displaystyle {^{n}a}}$ means ${\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}}$, where n copies of a are iterated via exponentiation, right-to-left, I.e. the application of exponentiation ${\displaystyle n-1}$ times. n is called the "height" of the function, while a is called the "base," analogous to exponentiation. It would be read as "the nth tetration of a".

Tetration is also defined recursively as

${\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}}$,

allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers.

The two inverses of tetration are called the super-root and the super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary.

Tetration is used for the notation of very large numbers.

🔗 Mathematics

The Erdős number (Hungarian: [ˈɛrdøːʃ]) describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.

🔗 Mathematics

A hinged dissection, also known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged" points, such that the rearrangement from one figure to another can be carried out by swinging the chain continuously, without severing any of the connections. Typically, it is assumed that the pieces are allowed to overlap in the folding and unfolding process; this is sometimes called the "wobbly-hinged" model of hinged dissection.

🔗 Mathematics 🔗 Statistics 🔗 History of Science

Stigler's law of eponymy, proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication Stigler’s law of eponymy, states that no scientific discovery is named after its original discoverer. Examples include Hubble's law, which was derived by Georges Lemaître two years before Edwin Hubble, the Pythagorean theorem, which was known to Babylonian mathematicians before Pythagoras, and Halley's Comet, which was observed by astronomers since at least 240 BC (although its official designation is due to the first ever mathematical prediction of such astronomical phenomenon in the sky, not to its discovery). Stigler himself named the sociologist Robert K. Merton as the discoverer of "Stigler's law" to show that it follows its own decree, though the phenomenon had previously been noted by others.

🔗 Mathematics

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules proves everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.

The paradox is named after the logician Haskell Curry. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.

🔗 Mathematics

The Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines if a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S where S is isomorphic to the projective line.

The algorithm was first published in the 1979 paper "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker, and it was later named the "Cox–Zucker machine" by Charles Schwartz in 1984. The name is a homophone for an obscenity, and this was a deliberate move by Cox and Zucker, who conceived of the idea of coauthoring a paper as graduate students at Princeton for the express purpose of enabling this joke, a joke they followed through on while professors at Rutgers five years later. As Cox explained in a memorial tribute to Zucker in Notices of the American Mathematical Society in 2021: "A few weeks after we met, we realized that we had to write a joint paper because the combination of our last names, in the usual alphabetical order, is remarkably obscene."

🔗 Biography 🔗 Mathematics 🔗 Biography/science and academia 🔗 Chicago 🔗 Armenia

Alexander (Smbat) Abian (January 1, 1923 – July 24, 1999) was an Iranian-born Armenian-American mathematician who taught for over 25 years at Iowa State University and became notable for his frequent posts to various Usenet newsgroups, and his advocacy for the destruction of the Moon.

🔗 Mathematics

The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error.

This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory.

🔗 Mathematics

The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though it is not convenient for writing software. Instead, it is important in the mathematical theory of algorithms because it is an extremely simple Turing complete language. It can be likened to a reduced version of the untyped lambda calculus. It was introduced by Moses Schönfinkel and Haskell Curry.

All operations in lambda calculus can be encoded via abstraction elimination into the SKI calculus as binary trees whose leaves are one of the three symbols S, K, and I (called combinators).