45 votes

How did the Romans do division?

The short answer, according to Turner (1951), is: we don't know. The Romans were not interested in recording theoretical mathematics, so we don't have any written accounts how they did it. It is ...
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  • 3,839
37 votes

How did the Romans do division?

The usage of using numerals for division neither existed nor was it necessary. Symbols were only used for recording results. This also explains why the romans used their system because it is easy for ...
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  • 5,018
30 votes

How did the ancient Romans count with their fingers?

This page displays many Roman era testimonies that there was a system, and that it served to count at least up to the hundreds. I'll copy here the most important ones. Juvenal in his Satire X, 246 ...
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28 votes

How did the ancient Romans count with their fingers?

All the sources clearly state that there is no actual record of how Romans performed mathematical calculations. However it is well established that the Romans knew of, and used, the abacus. It is ...
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23 votes

What was the first solar eclipse that was demonstrably predicted in advance?

(This is an incomplete answer since I don't know which eclipse specifically was predicted, nor how it compares to the rest of the world. But it is too long for a comment.) Because of their cultural ...
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  • 96.2k
17 votes

How could Eratosthenes measure the circumference of the Earth?

He synchronised them to the solar zenith. Eratosthenes knew that on the day of the summer solstice, the sun passed vertically above Syene, which lies very close to the Tropics of Cancer. As the ...
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  • 96.2k
16 votes

How did Columbus calculate the size of the Earth?

Well, Columbus case is one hallmark how to cherry-pick your data to come to desirable conclusions. Columbus began with the values of the best sources available: from the Arabian astronomer al-...
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  • 5,018
15 votes
Accepted

Study of causal structures and dynamics in history?

There is an emerging trans-disciplinary field called cliodynamics which studies these ideas. There's an open access journal, Cliodynamics: The Journal of Quantitative History and Cultural Evolution, a ...
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  • 28.1k
13 votes

Why are doughnuts toroidal?

An article from the Smithsonian magazine titled "The History of the Doughnut" also states that Captain Hanson Gregory invented the toroidal doughnut. The reason for the invention seems less clear. The ...
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  • 76.4k
13 votes

Before European influence circa 1600, did any Chinese believe the Earth was spherical, and did they ever try to measure it?

See Joseph Needham's momumental work : Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth, Cambridge UP (1959), page 212-213: "Rather ...
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12 votes

Did the Babylonians know the Pythagorean Theorem before Pythagoras formulated it?

As far as we know, Babylonians had no Pythagorean theorem and no theorems at all whatsoever. The major contribution of the Greeks was that "there are statements (which they called theorems) which can ...
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  • 37.5k
11 votes

Whatever happened to Turing's friend Arnold Murray?

It looks like you might want to read the book about Turing: Alan Turing : The Enigma by Andrew Hodges This is the book that the movie the Imitation Game was based on. In this book Hodges discusses ...
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  • 34.2k
10 votes

How many digits of Pi did the old Egyptians know?

The ancient Egyptians at the time of the Rhind Papyrus didn't really have the concept of Pi. The method they described for finding the area of a circle was to inscribe it within a square, and apply ...
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  • 110k
10 votes
Accepted

Teaching of Mathematics in Italy and in Germany in the fifteenth century

tl;dr This is not a real story but an illustrative description, probably invented in the 1930s. The first Indo-Arabian numerals came to Europe in the 10th century. They had a hard time at first. In ...
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  • 77.2k
10 votes
Accepted

Has anyone created a binary calendar?

The core issue is that the purpose of a calendar is to track astronomical events, and in particular, their relations. The three that are universally tracked are the three that are obvious to anyone: ...
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9 votes
Accepted

Did the Babylonians know the Pythagorean Theorem before Pythagoras formulated it?

Is there any other evidence of this mathematical concept existing in Babylon before Pythagoras? Yes. As Wikipedia observes, the Plimpton 322 tablet … lists two of the three numbers in what are ...
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  • 76.4k
8 votes

How could Eratosthenes measure the circumference of the Earth?

Simple. While the earth moves around the year, the sun seemingly moves around between the Tropic of Cancer (north) and the Tropic of the Capricorn (south). In the north this is begin of summer and ...
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  • 5,018
8 votes

What is the earliest known writing associating the number three with the dimension of the world?

This is much more "obvious". It may well be even pre-historic. But since the question asks for written evidence: If you want mathematics, go like an Egyptian or Mesopotamian: A rectangular prism-...
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  • 77.2k
8 votes
Accepted

What does 'des' mean in ancient Egyptian?

Eric Peet, on page 117 of The Rhind Mathematical Papyrus offers what may be your explanation: So it would appear that des should describe the unit of liquid volume which would fill a des-jug, and ...
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  • 34.2k
7 votes

How did the Egyptian engineers of the Third and Fourth Dynasty construct the Pyramids and Sphinx without modern science and mathematics?

The site www.cheops-pyramide.ch is about how Egyptians were able to achieve an incredible precision when measuring with simple techniques. I'm going to summarize it. 1. Right angles in the corner ...
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  • 171
7 votes

What was the first solar eclipse that was demonstrably predicted in advance?

Wikipedia has an informative article on the Saros cycle, which is used to predict eclipses. According to that page, and by extension apparently the pages to which it references, the Babylonians were ...
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  • 1,904
7 votes
Accepted

When were Liu Hui's mathematical works first translated into English?

I assume the translation in question is The Nine Chapters on the Mathematical Art, which was indeed translated into French by Guo Shuchun and published in 2005. In fact, the first full English ...
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  • 76.4k
7 votes

What nationality was "Egbert Van Kampen"?

As one can deduce from the information provided in A Forgotten Mathematician, he was Dutch, confirming the Wikipedia claim. According to 1, Egbertus Rudolf van Kampen, known as Egbert, was born ...
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  • 6,030
7 votes

Who is the author of Romanoff's theorem?

See Romanov's brief bio in the Wikipedia article here. Use Google translate if you cannot read Russian. Note that there appears to be a small error in the article. Namely, according to the book "...
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  • 6,030
6 votes
Accepted

Was late-medieval French education recalcitrant to math?

Medieval scholarship was essentially a "great books" endeavor, where paragons of intellect were held to have the last word on many subjects (consider Aristotle for natural science or Galen for ...
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  • 1,734
6 votes
Accepted

What were the causes of decline of Babylonian numeric system?

Simply put, the decimal system is more convenient for most types of calculations. As you point out, there are systems that still use base 60. And there are others such as binary and hexadecimal which ...
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  • 3,314
6 votes

What were the causes of decline of Babylonian numeric system?

The Babylonian sexagesimal system is used by Ptolemy in his Almagest (2nd century AD) and by Arabic astronomers throughout the Middle Ages. The decimal numerals were introduced from India to the ...
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  • 9,473
6 votes

What was the first solar eclipse that was demonstrably predicted in advance?

From a NASA answer: Ptolemy ( ca 150 BC)[sic] represents the epitome of Greecian astronomy, and surviving records show that he had a sophisticated scheme for predicting both lunar and solar ...
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6 votes

Whatever happened to Turing's friend Arnold Murray?

Arnold was my uncle. He was convicted of homosexuality like Alan. I have read two books and they both have a different perspective of Arnold. He remained in Manchester and got married and had 2 kids. ...
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