# Tag Info

### What is Ptolemy holding in this picture?

This device was invented by a Jewish Rabbi, Levi Ben Gershon. It was used to measure the angular distance between two stars or, in general, any pair of celestial bodies. Ptolemy lived 1000 years ...
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### What is Ptolemy holding in this picture?

It is called "Jacob's staff". It was an old astronomical tool used for trigonometric purposes.
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### Did ancient Greek mathematicians consider numbers independently of geometry?

The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them) "numbers" were integers. "Rational numbers" were called fractions, and no ...
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### Why is one meter as long as it is?

This number has no significance. Its origin is historical. Originally the meter was defined as 1/40,000,000 part of the Paris meridian. Based on the measurement of this meridian, they made a standard ...
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### What is Ptolemy holding in this picture?

And this tool has been known under many other latin names than baculus Jacob (or Jacob's staff): radius astronomicus (astronomic ray), crux geometrica (geometrical cross), revelatorem secretorum (...
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### Who was the first to calculate $\pi$?

It depends on the meaning of "calculate", since $\pi$ is a transcendental number it can not be "calculated" in the usual meaning of the word. The first analytic formula (in the form of an infinite ...
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### What is the etymology behind sine, cosine, tangent, etc.?

Victor Katz is not a linguist and a lot of what he says in the quoted extract is wrong: for example that “Arabic is written without vowels” and that the word in question is spelt “jb”. In fact it is ...
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### What is the etymology behind sine, cosine, tangent, etc.?

For sinus, see : Victor Katz, A History of Mathematics (3rd edition, 2008), apge 253 : The English word “sine” comes from a series of mistranslations of the Sanskrit jya-ardha (chord-half). ...
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### How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

For example, the very first proposition: Construct an equilateral triangle $ABC$, where one side $AB$ is given. Euclid says Draw a circle with center $A$ and radius $AB$. [By Postulate 1] Draw the ...
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### What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

Poincare refers to the Lie's solution of the so-called problem of space, a.k.a. the Helmholtz , or Riemann-Helmholtz, or Helmholtz-Lie problem of space, which amounts to characterizing all manifolds (...
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### What was the best approximation of π known to ancient Babylonians?

No additional or more precise approximations to $\pi$ seem to have been found in Babylonian records up till now. Herman C. Schepler, "The Chronology of PI", Mathematics Magazine, Vol. 23, No....
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### A knot cannot be tied in 4-dimensions, but when was this conjectured and proven?

A nice account is found in a note to R. Steiner's Die vierte Dimension (1995; translation): Felix Klein (1845–1925) seems to have been the first mathematician to draw attention to this phenomenon ...
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### How did Eratosthenes knew the exact time of the day?

The first sentence of the question is not justified. Accuracy of Erathosphenes measurement was much discussed in the literature, and it is certainly not "incredible". What the actual accuracy was is ...
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### How did Eratosthenes determine that Alexandria and Syene were on the same meridian?

We do not know. First, Syene and Alexandria are not on the same meridian, Alexandria is about 3° to the West, and second, Syene is not on the tropic (where the Sun is straight up on the summer ...
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### What is Poincare's "Fourth Geometry"?

It is the Minkowski plane, the lightlike lines are “perpendicular to themselves”, see e.g. Stachel, Poincaré and the Origins of Special Relativity. To get this geometry, one needs to ...
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### What mathematics did Isaac Newton learn at school?

Newton studied at school and at the university, but he mostly taught himself by reading. (At his secondary school he certainly learned Latin, Greek, the Bible and some arithmetic. In the universities,...
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### What did Delaunay invent Delaunay triangulations for before computers were developed?

Delaunay (Gallicized version of Russian Delone) did not invent them, they were used long before 1934. Delaunay triangulations, or more generally tesselations, are dual to Voronoi diagrams, the ...
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### Fibonacci and straightedge and compass constructions

In the Flos (Flos Leonardi Bigolli Pisani super solutionibus quarundam questionibus ad numerum et ad geometriam, vel ad utrumque pertinentium), Fibonacci reinterprets in algebraic form the geometric ...
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### What is the history of the meanings behind the word "Geometric"?

"Geometry" literally translates from Greek as "land measurement", and reflected a popular Greek belief that they learned it from Egyptian "rope stretchers", land meausurers, who used ropes to perform ...
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### Why did Newton want lines to be generated by continued motion of points rather than by apposition of parts?

Problem: classical geometry is not happy with infinitesimals Newton is systematically trying to avoid basing calculus on infinitesimal geometric quantities. We can see this from how he emphasizes ...
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### Why is Freeth's nephroid called a nephroid?

Doesn't look like a kidney? Freeth's nephroid $\qquad$
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### What are the earliest known proofs that planimeters 'work'?

Using planimeters to illustrate Green's theorem is a relatively recent didactic development. Neither Green, nor Cauchy, nor Riemann had any interest in the instruments, and vice versa, planimeter ...
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### How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

The main difference is that Mathematical logic and set theory did not exist at the time of Euclid. (The Logic of Aristoteles is still very far from mathematical logic created in 19th century). As a ...
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### Who was the first to calculate $\pi$?

What do you mean "correctly or not"? Here is a brief history. The Bible has a sentence which can be interpreted as implying that $\pi=3$. The EXISTENCE of $\pi$ (the ratio of circumference to ...
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### When did mathematician start to draw figures from equation?

The coordinate method may be traced to antiquity, specifically to the works of Apollonius of Perga (c. 262 – c. 190 BC) The following quotation from Carl B. Boyer,"Apollonius of Perga" (1991). A ...
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### What does "given in species" mean in old geometry textbooks?

Such terms as “given in species” are defined in Euclid’s Data (Greek, English): III. Rectilineal figures are said to be given in species, which have each of their angles given, and the ratios of ...
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### Who was the first to calculate $\pi$?

Since the question specifically says "to any accuracy," I will assume you mean approximations as well. In this case, the first recorded approximation of $\pi$ comes from the Babylonians, who not only ...
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### What topological ideas did Gauss introduce to his student Möbius?

While you already accepted an answer, it seems not superfluous to add another one, in particular since you are implicitly asking for a better translation/understanding of the passage you quoted. ...
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### Has Euclid stated Cauchy's theorem?

I found it. It is Definition 10 in Book XI. https://mathcs.clarku.edu/~djoyce/elements/bookXI/defXI9.html Euclid takes the assumption of Cauchy's theorem as the definition of equality of polytopes! ...
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