Questions tagged [terminology]
For questions about terms, definitions and related concepts used in science and mathematics.
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What changes in mathematics resulted in the change of the definition of primes and exclusion of 1?
Why 1 is not prime? I read in this article that G.H Hardy explicitly included 1 as a prime in the first 6 editions of "A Course in Pure Mathematics", published between 1908-1933. He updated ...
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How did Gaussian and Eisenstein integers get their names?
I can separate this into two questions at some point if necessary, but it's possible that sources for the answer to one will provide the answer to the other at the same time.
I learned about ...
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Have orthogonal complex matrices appeared in the literature?
According to https://en.wikipedia.org/wiki/Orthogonal_matrix,
https://en.wikipedia.org/wiki/Unitary_matrix, and
Friedberg et al.'s Linear Algebra (4th edition), a matrix $A\in F^{n\times n}$
is ...
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What was the significance of Eisenstein's discovery of invariants?
I am trying to decipher a portion of James Joseph Sylvester's 1869 address entitled "The Study That Knows Nothing of Observation", which, among other things, surveys the landscape of 19th century ...
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Why are there so many German terms in the field of radiative transfer?
A lot of phenomena in radiative transfer are named after a person who studied them (Rayleigh scattering, Mie scattering, Bragg diffraction, Kikuchi lines, Tyndall effect,...). Others are designated by ...
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Where does the name "geometric sequence" come from?
On this and other Stack Exchange website, there have been question about the so-called geometric series, and where its name comes from. My problem is that most answers follow one of two different ...
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Why was the 'differential entropy' from information theory so named?
The entropy of a distribution $p$ on a discrete set $\mathcal{X}$ is defined as $$H(p) = -\sum_{x \in \mathcal{X}} p_x \log p_x.$$ Shannon in his classic paper [1] defines the analogue for continuous ...
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Grassmann Formula
I'm in my first year of Mathematics at the University. Recently, we've learnt about Grassmann Formula and when I was making a little research on the internet, I couldn't find a single reference ...
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Who are credited for angle transformation formulae and law of sines in trignometry
I'd like to who are credited for discovering angle transformation formulae
$$
\sin(A\pm B)=\sin(A)\cos( B)\pm\cos(A)\sin(B)
$$
$$
\cos(A\pm B)=\cos(A)\cos( B)\mp\sin(A)\sin(B)
$$
$$
\tan(A\pm B)=\...
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What is the origin of "law of excluded middle"?
Reading an article I have stumbled across the concept of law of excluded middle.
Wikipedia mentions that original expression is principium tertii exclusi which ...
Alexei
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Hamiltonian $H$ named after Huygens?
This seems an unlikely origin of the abbreviation $H$ for Hamiltonian. Is there evidence for this nomenclature?
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Where does "the grating equation" come from? Does it have a another name?
What we often refer to as Snell's law:
$$n_1 \sin(\theta_1) - n_2 \sin(\theta_2) = 0$$
has quite a bit of history behind it. It can be demonstrated in several ways, one of which is by asserting that ...
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Who coined the term "immune system"?
Who coined the term "immune system"?
The OED lists the following as its earliest example of the term "immune system":
1943 Science 30 Apr. 406/1Complement..is removed by the addition of an ...
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Why is the SI prefix k- lower case?
In the SI unit prefixes, there's a general pattern of using uppercase prefixes for multipliers larger than 1 and lower case for prefixes that are smaller than one. However, this is not a universal ...
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Were integrals really called solution curves (or vice versa)?
For some reason I recall hearing that around the time Euler wrote his Calculus books (1768-1770), or even before then, what we call integrals now were called solution cuvres (or even possibly the ...
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Origin of the terminology “trace operator” related to boundary-value problems for PDEs
Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator (not to be confused with the trace from linear algebra) essentially ...
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Analysis vs Synthesis in Greek Mathematics
I am trying to understand the difference in "analysis" and "synthesis" as used by the ancient Greek mathematicians. Most sources characterize synthesis as working from givens to a desired conclusion, ...
user3339
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Etymology of certain terms in the theory of elliptic integrals
In the theory of elliptic integrals, one encounters the terms "amplitude" and "modular angle" in relation to incomplete integrals of the first kind, which are two variables that denote the upper limit ...
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Origin of the word "vector" [closed]
I would like to know the history and the original meaning of the word "vector". Thank you for any hints.
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What did Dedekind's The Nature and Meaning of Numbers contribute to the founding of Set Theory?
As best as I can tell Dedekind's paper was published in 1887 already several years after Cantor's flurry of papers on Set Theory between 1879-1883. With this in mind my central questions are:
1) What ...
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Who coined the 'particle zoo' expression?
I've been looking for the origin of the 'particle zoo' expression but so far failed to track down who first used it or at least who popularized it.
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Who assigned the name "work" to the quantity $\int F\,{\rm d}r$?
I am looking into the historical perspective of how the concept of work and energy came about: who coined the terms "mechanical work" and "energy", and how the concept evolved over time.
I know that ...
Rajneesh Singh
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Terminology associated with mathematical induction
In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...
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How did the terms stress and strain come to describe two different things?
In physics, stress essentially captures forces in a body, where as strain captures displacements. Two dimensionally very different concepts. If you look it up in a thesaurus, stress and strain are ...
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Who was the first to use the term field in physics?
Faraday, after drawing his lines of force in 19th century, is normally credited as the first to use the term field in physics. But...
... was not the term field used in the context of gravitational ...
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On early US patriotism to choose quark color charge labels
Sean Carroll has a video about gauge theory (2020) in his series about Greatest Ideas of the Universe, where he claims that early in the development of quantum chromodynamics, some physicists tried to ...
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Who Invented The Number Line?
Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?
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Why is it called the butterfly effect?
The pop-sci answer is that Lorenz characterised chaotic atmospheric dynamics with the hypothetical example of a butterfly's flapping wings changing whether a tornado results. However, since butterfly-...
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What word meaning "random" was used before the word "random" got popularized?
In the What is Random? vlog of the Vsauce channel, Michael says (start from 3:25):
In the 1300s, random meant running or at great speed. Later, it would be used to describe things that have no ...
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Why is the letter $b$ used to represent the y-intercept in the equation of straight line?
The slope-intercept form of a non-vertical line is $y=mx+b$. I have been told that the slope is called $m$ because it is the first letter of the French word for mountain. But why is there the letter $...
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First mention of Fundamental Theorem of Arithmetic
Without a Disquisitiones Arithmeticae at hand, I may ask... When the unique factorization theorem was first called the Fundamental Theorem of Arithmetic?
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Origin and use of the adjective "improper" in mathematics
Anybody with elementary mathematical education will have seen improper fractions to refer to fractions where the numerator is greater than or equal to the denominator.
At a certain point in calculus ...
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Why are permutations ($_nP_r$) called differently in non-English languages ("variations" in German)?
First of all, you should be at least a little familiar with combinatorics to understand that question.
Some often used calculator keys in stochastic are the nCr and nPr ones.
Edit: I've first asked ...
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When was a partition of unity discovered?
A partition of unity is a mathematical concept in geometry. I want to know when and in what context this concept appeared.
user5146
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Do the words 'graphing' a function and 'graph' theory have a common ancestor?
When saying graph in mathematics, it can be either a graph of a function, or a graph in graph theory. However mathematically they have nothing in common. How did they get the same name?
I know graph ...
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How long have people been debunking the P value (statistical significance) as commonly used in the human sciences: medicine, psychology and so on?
I have been puzzled for a long time at the way psychologists and medical researchers state that they have 'significant' results, and at the way this statement is relayed to the public who are misled ...
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What is the etymology of the term "mode" in statistics?
I saw that the word "mode" means "popular" in French, and I was wondering if this might be the etymology of the "mode" of a population in stat?
I was wondering if anyone had sources for early use of ...
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Name of the Gamma function
The Gamma function for positive arguments can be defined with the integral
$$ \Gamma(\alpha) = \int_0^\infty x^{\alpha-1} e^{-x}\,dx $$
The function $ x^{\alpha-1} e^{-x} $ is called the Gamma ...
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Introduction of $\imath$ and $\jmath$ notations for the imaginary unit
The imaginary unit is generally denoted $i$ or $\imath$. I have learned that the term imaginary ("imaginaires") was coined by R. Descartes in 1637, and the "i" notation was introduced by L. Euler (cf. ...
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Jordan called isomorphisms (iso.) and homomorphisms "iso. holoedriques" and "iso. meriedriques" respectively; translation of holoe/meried-driques?
Stillwell mentions in his Elements of Algebra:
The first to use the term "isomorphism" was Jordan, in his Traite des Substitutions [1870], the first textbook on group theory...Jordan used the word "...
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Who came up with the name "Manhattan distance"?
Who came up with the name "Manhattan distance" (for the distance between two points as measured by the sum of the horizontal and vertical distances, as opposed to the length of the straight ...
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Why are the first three multiplicative SI prefixes lowercase?
The BIPM specifies twenty prefixes for the International System of Units (SI). All ten of the fractional prefixes are lowercase. However, only seven of the multiplicative prefixes are uppercase, the ...
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What is the etymology of lower case p as the operator for the negative of the common logarithm?
In high school we were taught that the formula for pH is the negative of the common logarithm of hydrogen ion concentration: pH = -log[H+].
It wasn't until I took organic chemistry that the "acid ...
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Why are complex numbers called 'complex'?
I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained.
I also ...
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Who first gave a definition of congruent triangles?
Who was the first to define congruent triangles? I couldn't find the definition in Euclid's Elements.
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How did the early chemists make a connection between gram formula weight with 1 mole and Avogadro's number?
According to one historian Mustafa Sarikaya's article in Foundations of Chemistry DOI 10.1007/s10698-011-9128-7, the mole concept was introduced to chemistry earlier than Avogadro’s number. The mole ...
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Why and who was the first to denote the square root operation in fractional form as $1/2$
Basically, the square root operation was discovered and proved rigorously from the Pythagorean theorem, it was denoted by square root of a rational number say $n$ as $\sqrt{n}$, but at a later stage, ...
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First use of litte $o_p$ (little $o$ in probability) notation?
I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this ...
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Origin of use of "quotient" to describe structures induced by equivalence classes
I'm sure this question has been asked somewhere, but I have been unable to find it. Why is it that when we have some set $X$ with an equivalence relation $\equiv$, and $X$ has some structure (e.g. a ...
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Origin of the expression "Open problem"
Google Ngram shows that the expression "open problem" started to be in use around the end of the 19th century.
My question is then 2-fold:
Who coined the expression? Wikipedia doesn't seem ...
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