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44

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 ...


35

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

If the following seems too long, you can directly jump at the end for the conclusion ins the TL;DR section. I'm not an historian and (almost) everything I tell below comes from internet research. More precisely, the whole stuff I tell below finds its source in various articles by the assyriologist Jens Høyrup. The king and the chess board in Indian and ...


27

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 ...


26

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 ...


23

Eratosthenes' calculations did turn out to be quite accurate. This was mostly a matter of luck though. He in fact had two major errors, that just happened to cancel each other out. It is also a fact that nobody is sure how big his unit of distance was, and it is only now after the fact that we can take one of the possibilities and say he was only 2% off. It ...


21

Tally sticks were credit-based money used by the King of England from roughly the XIII to the XIX century. The idea was quite simple: in a credit based system, you have to find a way to represent the credit which is uncounterfeitable and cheap to produce. It also had to have no value as an object, otherwise you can have a market for the object rather than ...


19

(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 ...


18

I found about 50 different sources for your quote, all verbatim copies of each other and without any indication of which those tablets were, who discovered them or any hint to catalogue numbers. I truly hate the internet sometimes, please treat this answer as a guess, there's no way to verify exactly which tablets the quote is about. One of the tablets is (...


16

The earliest record (I have) found (searching the Internet) is the Persian Book Shahnameh, of which I know nothing more than the Wikipedia entry: The Shahnameh or Shah-nama (Persian: شاهنامه‎ Šāhnāmeh, "The Book of Kings") is a long epic poem written by the Persian poet Ferdowsi between c. 977 and 1010 AD and is the national epic of Iran and related ...


15

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, ...


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 ...


14

The 1877 work by Richard Lepsius entitled Die Babylonisch-Assyrischen Langenmafe Nach Der Tafel Von Senkereh states that the two tablets you refer to (of squares and cubes) were discovered by Loftus in 1854 and at that time they were in the collection at the British Museum. It also states that Rawlinson and Smith's work of 1875 on cuneiform inscriptions, ...


14

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 ...


12

They used lots of very large, very heavy stones. You will note that these constructions did not have large internal air pockets relative to volume. They qualify as monuments or fortifications more than inhabitable buildings with a decent amount of floorspace. Having arches or domes or any large enclosed internal space was considered the height of ...


12

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 the ...


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

You weren't kidding. I found those exact two sentences plagerized verbatim all over the Internet. Truly sad. I did manage to find a least a couple of references with more information though. The Handy Math Answer Book was not only original enough to modify the sentence a bit, but included some alternate dates, and a very nice extra aside about one object ...


10

Johannes of Palermo was a scholar in Frederick II's court. Frederick was aware of Fibonacci's work, and perhaps even an admirer. In 1225 when Frederick's court met in Pisa, Fibonacci was invited to demonstrate his works. I can't find a source for when exactly Johannes of Palermo posed his problems, but the two men certainly met in Pisa and Johannes posed his ...


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....


9

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 ...


9

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 ...


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

According to this article, Pope Sylvester II (Gerbert d'Aurillac, c943-1003), is credited with re-introducing the abacus into Europe without an explicit use of the number zero. This was because it had not been introduced in the European mathematical vocabulary (Fibonacci did this around 1202, and it took centuries for it to become established), rather than ...


8

Yes, there was such a bill, known as Indiana Pi Bill, but it was never approved by the State. You can find a very interesting article on the matter, written by Arthur E. Hallerburg, in the text of Proceedings of the Indiana Academy of Science. Search for the phrase House Bill No. 246 Revisited. The whole affair started in 1894, when American Mathematical ...


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

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, ...


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 ...


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