45

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 assumed that whatever they knew was learned from the Greeks, but alas there is no Greek account (from the period) of a pure number division either, only of one ...


36

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 recording. Big numbers first and easy to remember symbols for the different steps of 100,50,10,10,5,1. The operations itself were calculated by an abacus. ...


30

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, 246 251, referring to Nestor, famous in Antiquity for his longevity, clearly implies that units and tens were counted on the left hand and the hundreds were counted ...


28

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 also trivial to see how the Roman Numeral system was a literal representation of the results shown on the abacus in non-subtractive mode. Finally, it is well ...


23

(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 association of governmental legitimacy with astronomical/geophysical omens, ancient China was rather obsessed with predicting eclipses. Attempts to do so seemed ...


17

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 traditional account goes, the sun was directly above a vertical well at Syene, whereas at Alexandria the columns of the Library always leaves a shadow. Either way, ...


16

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-Farghani. Al-Farghani calculated very carefully that the distance of one degree latitude (north-south) equals 56 2/3 arabian miles (1972 m) which is 111.8 km; the ...


15

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 lab in England, and an institute in New Mexico. Cliometrics is somewhat related: it applies the ideas of economics to the study of history. It's been around ...


13

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 article notes that: Some cynical doughnut historians maintain that Captain Gregory did it to stint on ingredients, others that he thought the hole might ...


13

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 characteristically Chinese, however, was the insistence that the heavens were circular and that the earth was square, an idea which would arise naturally enough from ...


12

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 be PROVEN". This was a unique discovery, and no trace of it exists in any other culture. The notion of a "theorem" is a Greek invention, and there is absolutely ...


11

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 interviewing Murray in 1980, and there appear to be several pages discussing the relationship. The book, on page 675 mentions Murray feeling guilty after ...


10

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 the ratio of 64/81 to the area within the square. However, we know today this is mathematically equivalent to using a Pi of 256/81. That's a hair smaller than 3....


10

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: The rotation of the Earth The movement of the Moon around the Earth The movement of the Earth around the Sun. The issue is that these time periods do not ...


9

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 the 13th century the Italian Leonardo Fibonacci published the Liber abaci (1202) which popularised their use further, but mainly in Italy. In 1522 Adam Ries then ...


9

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 now called Pythagorean triples, i.e., integers a, b, and c satisfying a2 + b2 = c2 (Click to enlarge) In addition to the Plimpton 322 tablet we have: The Yale ...


8

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 the sun reaches the highest point. The first city where the deep well exists is the city of Syene (now Assuan) which is almost exactly on the Tropic of Cancer, ...


8

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-grain silo has a volume of 2500 quadruple heqats. Describe its three dimensions l1, l2, l3 in terms of cubits. From Rhind-Papyrus (It dates to around 1550 BC ––...


8

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 that unit is unique (or at least originally referred to) to an item of the particular design of the des-jug.


7

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 The base of the Cheops pyramid forms a perfect square - the deviation from the 90° angle is a maximum of one minute, which is very precise when you consider the ...


7

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 recording the eclipses which describe the cycle in the sixth century BC. Apparently Hipparchus (second century BC), Pliny (first century AD) and Ptolemy (second ...


7

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 translation of The Nine Chapters on the Mathematical Art wasn't published in English until 1999, although abridged translations were published much earlier. The ...


7

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 on 28 May 1908 in Berchem as the youngest in a family of three children. Egbert’s parents had moved from the Netherlands to Belgium a couple of years before, ...


6

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 medicine). For mathematics, the Quadruvium included Arithmetic and Geometry (heck, that was two out of four), where Nicomachus and Euclid were the 'paragons' for ...


6

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 eclipses. Ptolemy knew, for example, the details of the orbit of the Moon including its nodal points, and that the Sun must be within 20d 41' of the Node point, and ...


6

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 are applied in other areas where they are applicable. But the main reason for its decline is the unwieldiness. 60 as a base is difficult to use because you ...


6

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 Muslim World in the 9th century AD, and later from the Near East to Europe. It took a long time for the “Indian” numbers to be accepted, but eventually people ...


6

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. They split up. He moved away to London and got married again and had 2 more kids. The relationship broke down. He was a musician who had work published. He did ...


6

TL;DR According to Roger Hart [1], this view is widely held but wrong. He cites, among (many) others, Needham who speaks of a decay and Mikami who considers Ming scholars to be degenerate. The alleged reason is not a decree, but societal and technical characteristics of the society. This view is slow to revert, because almost no one studies Ming mathematics, ...


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