Questions tagged [notation]

For questions about the history and development of how symbols and related objects are written.

Filter by
Sorted by
Tagged with
12
votes
1answer
1k views

How did mathematicians notate the empty set before $\varnothing$?

I recently learned that $\emptyset$ or $\varnothing$ is a relatively new notation for the empty set created in 1939. I know $\{\}$ is also used along with $\{\cdot\}$ to denote empty sets. What was ...
14
votes
2answers
8k views

What is the origin of polynomials and notation for them?

This may be quite a broad question, but lately I've been wondering about the history behind polynomials. Nowadays these are pretty much the simplest kind of functions to work with, but I'd like to ...
7
votes
2answers
397 views

Where did Cartan introduce his notation for basis vectors and covectors?

There is a notation used in differential geometry and general relativity in which the partial derivative operators $\partial_\mu$ are used as the basis for the space of contravariant vectors, and ...
5
votes
1answer
2k views

How did the theory of the Horus-eye fractions originate?

In a book, I saw a short anecdote about something called the "Horus-eye" hieroglyph, supposedly used in parts to represent fractions (the book dates to 1997). Wikipedia has an article on the symbol ...
3
votes
0answers
66 views

Origin of alternate base annotation

In modern arithmetic textbooks, students are taught about alternate numeric bases. The notation for indicating the base of a number is to attach the base as a subscript. The subscript is itself a ...
12
votes
3answers
349 views

Why did Cantor (and others) use $\mathfrak{c}$ for the continuum?

Kontinuum is German for continuum, but Cantor used $\mathfrak{c}$. Revision. J.W.Perry questions whether or not Cantor ever in fact used the symbol $\mathfrak{c}$. I must admit I just assumed that he ...
7
votes
4answers
2k views

Why is calculus missing from Newton's Principia?

I'm not suggesting that Newton did not discover calculus - the question is written this way to express my surprise that the Principia does not use the methods of calculus (or 'fluxions'). He instead ...
7
votes
1answer
223 views

When did the use of the comma as a decimal mark become extinct in the US?

The US and the UK uses a baseline dot as the decimal mark. Most other European countries use the comma. Here is a short piece on the history of this matter. My question is: When did the use of the ...
5
votes
1answer
514 views

Were there alternative names for electron orbitals?

Electrons orbits are referred to as s, p, d, and f, then alphabetically. These stand for sharp, principal, diffuse and fundamental respectively (or maybe the German translations). Was any other ...
1
vote
1answer
359 views

Why was the reduced Planck constant introduced and when?

When was the reduced planck constant $\hbar= h/2\pi$ first introduced and what was the reason behind introducing such a constant? I know that $E=\hbar \omega$ and $p=\hbar k$ and writing again and ...
30
votes
3answers
4k views

Writing Mathematical Symbols in 20th century

As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
19
votes
1answer
2k views

Why is the radical symbol $\sqrt{}$ called “radical”?

This question arose in a conversation with a teacher who was introducing square roots to her students. I know from the website Earliest Uses of Symbols of Operation that the symbol $\sqrt{}$ has its ...
9
votes
2answers
5k views

Why was delta ($\Delta$) chosen to represent change of a quantity?

In many fields, it's common for $\Delta$ (the Greek letter delta) to represent a change or difference. Math uses it, physics uses it, engineering uses it, etc. Why was $\Delta$ chosen for this? I ...
8
votes
5answers
1k views

Has a digit ever been used to represent the number “10”?

Ten is special to humans, as there are 10 fingers on two hands, and fingers are still the basic counting medium for people. So, was there any digit representing the number "10" in a positional system ...
5
votes
1answer
347 views

Modern usage of alchemical symbols

As far as I know, not many (if any) alchemical symbols have survived in modern nomenclature of science, either in chemistry or any other. I think $\LaTeX$ doesn't even support most of them! I know ...
11
votes
5answers
775 views

Why is the notation $\sin^{-1} x$ so common?

$\sin^{-1} x$ means the inverse of $\sin x$ (it is also often called $\arcsin x$), but it can fairly easily be confused with $\sin(x)^{-1}$. Why is it used, when $\arcsin x$ is easier to type and is ...
10
votes
1answer
10k views

Who invented short and long division?

I am curious who came up with algorithms that we use today to manually solve mathematical division problems, such as short or long division; how were they established or standardized that way and why?...
3
votes
0answers
319 views

How was the use of upper and lower indices in tensor notation developed?

It is just a notation, but it is so economical and so systematic. So who invented them? A handy notation should be helpful for the development of the whole field.
1
vote
0answers
50 views

Use of $h$ in the Newton Quotient [duplicate]

Why do we typically use $h$ for $$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ A student asked me this the other day. My guess was that it was originally height, because ...
6
votes
4answers
184 views

Use of $h$ in the Newton Quotient

Why do we typically use $h$ for $$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ A student asked me this the other day. My guess was that it was originally height, because ...
9
votes
1answer
2k views

Who really invented the integration symbol?

Most of the sources online say that Leibniz invented the sign. There's also this answer on this site which says so. That is fine. But recently when I was watching Cosmos, I noticed this: See the ...
13
votes
1answer
831 views

When was the vector notation in physics and other sciences first introduced?

The vector notation in physics is a very compact and easy way to write things down, and according to Feynman it also saves print. When exactly did scientists realize that they were summarizing things ...
18
votes
1answer
5k views

Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
18
votes
2answers
1k views

Who invented the way we write exponentiation?

Why do we write $a^n$ instead of $^n\!a$ for exponentiation? What benefit is there to writing the base before the exponent? With addition and multiplication order doesn't matter since $a + b = b + a$, ...
32
votes
1answer
1k views

What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?

[Mauro Allegranza has answered the question of who introduced the notation $i$ (Euler, followed later by Gauss), so I have changed the title. I have also edited the question in other ways to make it ...
8
votes
1answer
153 views

When was the short notation for large numbers first introduced and why?

While the long notation or long scale uses multiples of millions to denominate larger numbers (e.g., 10^12 being a billion, a million of millions, thus bi-llion), the short notation (the standard in ...
27
votes
1answer
2k views

Why is American and French notation different for open intervals (x, y) vs. ]x, y[?

The Americans and the French use a different notation for open intervals: The Americans use (x, y) while the French use ]x, y[. How did this notational divergence appear?
23
votes
3answers
28k views

Why is price on the vertical axis and quantity on the horizontal axis?

In most of science, it is typical to have the independent variable on the horizontal axis and the dependent variable on the vertical axis. But in economics, this is often (traditionally?) flipped ...

1 2 3