# All Questions

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### Why does Eratosthenes method for calculating the circumference of the Earth requires the city of Alexandria and Syene to be in the same meridian?

I'm reading a book where the author claims that in order for the method of angles and proportions used by Eratosthenes to work, the two cities would have to be located in the same meridian, or at ...
• 113
95 views

### Historical examples of frauds discovered because someone tried to mimic a uniform random sequence

So, I'm preparing a talk about the well known fact that humans are bad at the task of generating uniformly random sequences of numbers when asked to do so. I would like to spice the talk a bit by ...
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1 vote
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### The origin and use of the term "equianharmonic" (elliptic function)

In Weierstrass notation, the principal elliptic function $\wp$ is a solution of the differential equation $$(\wp')^2= 4\wp^3 -g_2\wp -g_3.$$ The case when $g_3=0$ is called lemniscatic (it ...
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80 views

### How and when did scientists first determine that hydrogen was the lightest element?

Cavendish first isolated hydrogen and recognized it for what it was; Lavoisier realized that water consisted of hydrogen and oxygen; Dalton used hydrogen as the basis for relative atomic weights by ...
1 vote
42 views

### Before metric length units were based on the speed of light, how were sub-units accurately derived from the reference bars?

Its my understanding that before metric units of length were based on the speed of light, there were reference bars that were used to calibrate other (mostly calibration) equipment. How were these ...
129 views

### What advances in statistics did measure-theoretic probability theory allow?

I've Googled this question in several different ways and I get a lot of hits, but nothing answering the question. To flesh out the subject line a little, I'm interested in understanding where, in the ...
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2k views

### Inscriptions on Newton's tomb

Whiteside in "The Mathematical Principles underlying Newton's Principia Mathematica" wrote .. if we can give credence to an account in The Postboy of 12 April 1731, his tomb in Westminster ...
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113 views

### Euler's "comfortable" series

I am reading Proofs and Confirmations by David Bressoud. On page $150$ is a long excerpt by Richard Askey, from "How can mathematicians and mathematical historians help each other?" There is ...
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### The role of symmetry in mathematics and the half-angle formulas

It seems that the most impressive theorems of classical geometry always have to do with "half of something". Consider the following examples: The three medians of a triangle meet at the ...
2k views

### How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors?

I have wondered if the apparently complex arrangement of the sails of early 19th century vessels was reflective of a lack of understanding of the optimal arrangement of such sails (since modern ...
• 1,041
1 vote
73 views

### Influence of Edmund Landau's list of four problems

At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers: Goldbach's conjecture, the twin prime conjecture, Legendre's conjecture (that there ...
• 1,068
199 views

### Gate 44 at the Colosseum in Rome: XLIIII or XLIV? When and why the change?

We teach our children in school that 4 is written in Roman numerals as IV and not as IIII but at the Colosseum in Rome, gate 44 is identified as XLIIII and not as XLIV. When did the change from IIII ...
132 views

### History of Speed - is it really new? [duplicate]

I was writing a paper on the basics of calculus, and of course the study of velocities plays a big part in that. In introducing the problem statement, I started with a classic word problem, "...
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1 vote
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### Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?

In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum'). Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
• 11
1 vote
173 views

### Motivation of the Hamiltonian formalism

In 1833 Hamilton introduced what today is called the Hamiltonian formalism in classical mechanics. I am wondering what was his motivation. Did he try to solve a specific question?
1 vote
100 views

### Why have advocates for positional number systems based on divisibility favoured base 12?

In the early twentieth century, with Esperanto and the like going on, a small movement called "dozenalism" began, with the aim of replacing base 10 with the purportedly more natural base 12. ...
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### question regarding Stern-Gerlach experiment

When Stern-Gerlach experiment was done with quantum electron , two peaks were observed rather than a continuous distribution as in case of small magnets , but how did those peaks confirm that angular ...
1 vote
68 views

### When did Abel publish his test for the convergence of series?

Did Abel published of testing the convergence of series? If so, when did he published it. Also, did he offer a proof of the test? Or did he simply stated the test?
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1 vote
93 views

### Bit as eighth of dollar vs Shannon's Binary Digit?

https://en.wikipedia.org/wiki/Bit#History does not mention the common usage of bit being an eighth of a dollar -- surely Shannon was inspired by this? This question was asked in 2019 in English ...
• 1,041
1 vote
49 views

### Development of Logic: Intuitive use vs what took so long to formalize?

I was encouraged in MathOverflow to ask this question here - so here it goes: As I am reading Frege and Boole, I am struck by that there doesn't seem to be a great alternative to Aristotle's Logic ...
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1 vote
84 views

### The symbol h for class numbers

We use $h_K$ conventionally to denote the class numbers of number fields $K$. But I have never thought why the letter $h$ was used for it. Why and who used $h$ for the class number?
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### How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

I am reading about the 1900s revolution of math pioneered by figures such as Hilbert. I have seen many articles speak very fondly of these figures due to the fact they tried to study Mathematics ...
138 views

### Early helium spectrum measurements and their challenge for Bohr's quantum mechanics

My understanding is that explaining ortho- and para- helium spectral lines was a key motivation for Heisenberg's new quantum theory. For example, Birthwistle's 1928 "The New Quantum Mechanics&...
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1 vote
174 views

### Was religion not present at all in the Astronomy of the Ancient Greeks?

I attended a lecture on the history of Astronomy and Mathematics, and I was somewhat puzzled by how scientific the early Greeks were. Yes, I am aware that they have many of the greatest mathematicians ...
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1 vote
151 views

### What does this quote by Paul Halmos mean?

I came across the following quote by the famous mathematician Paul Halmos: A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to ...
1 vote
145 views

### Who introduced the mixed fraction notation?

Who introduced mixed fraction notation? This notion is a source of confusion to me because it may be interpreted as multiplication.
118 views

### The first commutative diagram

Cf. https://golem.ph.utexas.edu/category/2013/07/the_first_commutative_diagram.html Is this the first ever commutative diagram? By commutative diagram I mean anything that shows an equality (or ...
283 views

I remember first seeing this anecdote a few years ago in a newspaper article, now I am seeing more frequently in motivational content over the internet, every time with very few additional details. ...
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232 views

### Anecdote about a seemingly possible, but actually impossible task given to students

There is a story I often tell my students about tasks that seem possible but are actually impossible, but I can hardly remember the details, and I am hoping that someone here would remember. Here is ...
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1 vote
83 views

### How did Euclid arrive at the law of reflection $r=i$?

The law of reflection, $r=i$, is attributed to Euclid. In his Optics text he refers to it, at the end of Page 360 in relation to Graph 19, and says he has demonstrated it in his Catoptrics. But I do ...
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