28
votes
Accepted
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 ...
- 50.5k
25
votes
Accepted
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 ...
- 50.5k
21
votes
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 ...
- 3,525
18
votes
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 ...
- 50.5k
16
votes
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). ...
- 15.1k
14
votes
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 ...
- 78.3k
14
votes
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 ...
- 10.5k
14
votes
Accepted
DeMorgan's commentary on Euclid's Elements
De Morgan's "Short Supplementary Remarks on the first Six Books of Euclid's Elements" is contained in the Companion to the (British) Almanac for the year 1849, pp.5–20, published by the ...
13
votes
Accepted
What is the origin of "two straight lines cannot enclose a space" axiom in Euclid's Elements?
It seems that the addition was made already in antiquity and motivated by the apparent gap in the proof of I.4. Rabouin in Proclus’ Conception of Geometric Space and Its Actuality writes:
"...
- 78.3k
12
votes
Accepted
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 (...
- 78.3k
11
votes
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....
- 7,189
11
votes
Accepted
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 ...
- 7,779
11
votes
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 ...
- 78.3k
11
votes
Accepted
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,...
- 50.5k
11
votes
Accepted
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 ...
- 78.3k
11
votes
Accepted
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 ...
- 78.3k
11
votes
Why did Columbus think the Earth was much smaller than it is?
Answering the earlier version of the question first (on Columbus mistakes).
There were two main sources of mistakes:
exaggerating the size of Asia and underestimating the size of the Earth.
Columbus ...
- 50.5k
11
votes
Accepted
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 ...
- 4,090
10
votes
Accepted
Why is Freeth's nephroid called a nephroid?
Doesn't look like a kidney?
Freeth's nephroid
$\qquad$
- 10.5k
10
votes
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 ...
- 50.5k
9
votes
Accepted
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.
...
- 690
9
votes
Accepted
How was Newton's classification of cubic curves completed?
Stillwell gives some details in Mathematics and its History. In modern terms, Newton made a general transformation of axes reducing the general cubic to four equation types, and then classified them ...
- 78.3k
9
votes
Accepted
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 ...
- 1,535
9
votes
What is the history of staircase or 𝜋=4 paradox?
The "staircase paradox" (or "Pythagoras paradox") name appears to be recent, so it is hard to search for it. Wolfram calls it "diagonal paradox", but that may be conflating it with a different paradox ...
- 78.3k
9
votes
Accepted
Did physicists correct an error of mathematicians in counting twisted cubics in the quintic?
Indeed they did, the OP story is told by Yau in The Shape of Inner Space, pp.169-70. Calculating the number of twisted cubics in the quintic hypersurface was a big early coup for mirror symmetry that ...
- 78.3k
9
votes
Accepted
Why is the letter $b$ used to represent the y-intercept in the equation of straight line?
The first known use of $b$ to represent the y-intercept in the equation of straight line is in Gaspard Monge's "Mémoire sur la Théorie des Déblais et des Remblais", Histoire de l'Académie ...
- 2,197
8
votes
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! ...
- 50.5k
8
votes
Accepted
Indiana Pi Bill: Other attempts to establish mathematical truth by legislative fiat?
It seems that this attempt made an impression, when one needs to make the point Indiana Pi itself is typically invoked. NMSR Reports modeled their 1998 April Fool's story on it:
"NASA engineers and ...
- 78.3k
8
votes
What are the modern connections of the Pentagramma Mirificum studied by Gauss?
The Pentagramma Mirificum is a spherical figure formed by a series of five great circle arcs, each orthogonal to the next, and it probably does deserve a Wikipedia entry. However some elementary ...
- 78.3k
8
votes
How did Eratosthenes determine that Alexandria and Syene were on the same meridian?
He may simply not have cared. A reasonably small distance along the east-west axis will only lead to a very small error in the distance along the north-south axis.
E.g. an azimuth of 190° instead of ...
- 181
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