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🔗 Mathematics

The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula.

In polar coordinates, with ${\displaystyle r}$ the radius and ${\displaystyle \varphi }$ the angle, the superformula is:

${\displaystyle r\left(\varphi \right)=\left(\left|{\frac {\cos \left({\frac {m_{1}\varphi }{4}}\right)}{a}}\right|^{n_{2}}+\left|{\frac {\sin \left({\frac {m_{2}\varphi }{4}}\right)}{b}}\right|^{n_{3}}\right)^{-{\frac {1}{n_{1}}}}.}$

By choosing different values for the parameters ${\displaystyle a,b,m_{1},m_{2},n_{1},n_{2},}$ and ${\displaystyle n_{3},}$ different shapes can be generated.

The formula was obtained by generalizing the superellipse, named and popularized by Piet Hein, a Danish mathematician.

🔗 Mathematics

In mathematics, the Bernoulli numbers B_n are a sequence of rational numbers which occur frequently in number theory. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function.

The values of the first 20 Bernoulli numbers are given in the adjacent table. Two conventions are used in the literature, denoted here by ${\displaystyle B_{n}^{-{}}}$ and ${\displaystyle B_{n}^{+{}}}$; they differ only for n = 1, where ${\displaystyle B_{1}^{-{}}=-1/2}$ and ${\displaystyle B_{1}^{+{}}=+1/2}$. For every odd n > 1, B_n = 0. For every even n > 0, B_n is negative if n is divisible by 4 and positive otherwise. The Bernoulli numbers are special values of the Bernoulli polynomials ${\displaystyle B_{n}(x)}$, with ${\displaystyle B_{n}^{-{}}=B_{n}(0)}$ and ${\displaystyle B_{n}^{+}=B_{n}(1)}$ (Weisstein 2016).

The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and independently by Japanese mathematician Seki Kōwa. Seki's discovery was posthumously published in 1712 (Selin 1997, p. 891; Smith & Mikami 1914, p. 108) in his work Katsuyo Sampo; Bernoulli's, also posthumously, in his Ars Conjectandi of 1713. Ada Lovelace's note G on the Analytical Engine from 1842 describes an algorithm for generating Bernoulli numbers with Babbage's machine (Menabrea 1842, Note G). As a result, the Bernoulli numbers have the distinction of being the subject of the first published complex computer program.

🔗 Biography 🔗 Korea 🔗 Biography/science and academia

Kim Ung-Yong (Hangul: 김웅용; born March 8, 1962) is a South Korean professor and former child prodigy, who once held the Guinness World Record for highest IQ, at a score of 230+.

🔗 Soviet Union 🔗 Russia 🔗 Russia/mass media in Russia 🔗 Television 🔗 Russia/history of Russia

Lenin was a mushroom (Russian: Ленин — гриб) was a highly influential televised hoax by Soviet musician Sergey Kuryokhin and reporter Sergey Sholokhov. It was first broadcast on 17 May 1991 on Leningrad Television.

The hoax took the form of an interview on the television program Pyatoe Koleso (The Fifth Wheel). In the interview, Kuryokhin, impersonating a historian, narrated his findings that Vladimir Lenin consumed large quantities of psychedelic mushrooms and eventually became a mushroom himself. Kuryokhin arrived at his conclusion through a long series of logical fallacies and appeals to the authority of various "sources" (such as Carlos Castaneda, the Massachusetts Institute of Technology, and Konstantin Tsiolkovsky), creating the illusion of a reasoned and plausible logical chain.

The timing of the hoax played a large role in its success, coming as it did during the Glasnost period when the ebbing of censorship in the Soviet Union led to many revelations about the country's history, often presented in sensational form. Furthermore, Soviet television had, up to that point, been regarded by its audience as conservative in style and content. As a result, a large number of Soviet citizens (one estimate puts the number at 11,250,000 audience members) took the deadpan "interview" at face value, in spite of the absurd claims presented.

Sholokhov has said that perhaps the most notable result of the show was an appeal by a group of party members to the Leningrad Regional Committee of the CPSU to clarify the veracity of Kuryokhin's claim. According to Sholokhov, in response to the request one of the top regional functionaries stated that "Lenin could not have been a mushroom" because "a mammal cannot be a plant." Modern taxonomy classifies mushrooms as fungi, a separate kingdom from plants.

The incident has served as a watershed moment in Soviet (and Russian) culture and has often been used as proof of the gullibility of the masses.

🔗 Psychology

The McCollough effect is a phenomenon of human visual perception in which colorless gratings appear colored contingent on the orientation of the gratings. It is an aftereffect requiring a period of induction to produce it. For example, if someone alternately looks at a red horizontal grating and a green vertical grating for a few minutes, a black-and-white horizontal grating will then look greenish and a black-and-white vertical grating will then look pinkish. The effect is remarkable because, where time-elapse testing is employed, it has been reported to last up to 2.8 months.

The effect was discovered by American psychologist Celeste McCollough in 1965.

🔗 Mathematics

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers.

Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x² − x + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has ever been proved to generate infinitely many primes, much less to have a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be.

In 1932, more than thirty years prior to Ulam's discovery, the herpetologist Laurence Klauber constructed a triangular, non-spiral array containing vertical and diagonal lines exhibiting a similar concentration of prime numbers. Like Ulam, Klauber noted the connection with prime-generating polynomials, such as Euler's.

🔗 Skepticism 🔗 Parapsychology

The Pauli effect or Pauli's Device Corollary is the supposed tendency of technical equipment to encounter critical failure in the presence of certain people. The term was coined after mysterious anecdotal stories involving Austrian theoretical physicist Wolfgang Pauli, describing numerous instances in which demonstrations involving equipment suffered technical problems only when he was present.

The Pauli effect is not related with the Pauli exclusion principle, which is a bona fide physical phenomenon named after Pauli. However the Pauli effect was humorously tagged as a second Pauli exclusion principle, according to which a functioning device and Wolfgang Pauli may not occupy the same room. Pauli himself was convinced that the effect named after him was real. Pauli corresponded with Hans Bender and Carl Jung and saw the effect as an example of the concept of synchronicity.

🔗 Computing 🔗 Computing/Software

"You aren't gonna need it" (YAGNI) is a principle of extreme programming (XP) that states a programmer should not add functionality until deemed necessary. XP co-founder Ron Jeffries has written: "Always implement things when you actually need them, never when you just foresee that you need them." Other forms of the phrase include "You aren't going to need it" and "You ain't gonna need it".

🔗 Psychology

Boredom boreout syndrome is a psychological disorder that causes physical illness, mainly caused by mental underload at the workplace due to lack of either adequate quantitative or qualitative workload. One reason for bore-out could be that the initial job description does not match the actual work.

This theory was first expounded in 2007 in Diagnose Boreout, a book by Peter Werder and Philippe Rothlin, two Swiss business consultants.

🔗 Business

A shotgun clause (or Texas Shootout Clause) is a term of art, rather than a legal term. It is a specific type of exit provision that may be included in a shareholders' agreement, and may often be referred to as a buy-sell agreement. The shotgun clause allows a shareholder to offer a specific price per share for the other shareholder(s)' shares; the other shareholder(s) must then either accept the offer or buy the offering shareholder's shares at that price per share.