The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [geometry]

The tag has no usage guidance, but it has a tag wiki.

Filter by
Sorted by
Tagged with
-1
votes
1answer
53 views

What was the chain of theories that led to relativity? [closed]

Can you briefly sketch the sequence of math theories that were necessary for Einstein to figure out a convincing background for relativity?
5
votes
1answer
131 views

When did mathematicians transition from peg and rope to straightedege and compass?

In the 19th and 20th centuries, the student of classical Greek geometry used "straight edge and compass". A. Seidenberg uses the terminology "peg and cord" in proposing that altar construction ...
7
votes
1answer
154 views

What is Poincare's “Fourth Geometry”?

In Science and Hypothesis, Poincare cryptically describes a "Fourth Geometry." Can anyone clarify what he is talking about? Is there a standard name for this geometry? The Fourth Geometry.—Among ...
3
votes
0answers
69 views

I want to know the source of why Archimedes' broken chord theorem is Archimedes good

I found "The Arabian scholar Abu'l Raihan al'biruni" has attributed to Archimedes the theorem of the broken chord in web. But I couldn't find a book or papers that this Arabian scholar wrote.
3
votes
1answer
131 views

Were people aware of the “mistakes” in Euclid's Elements before the start of the formalization of Mathematics?

For example, in proposition 1, Euclid assumes that the instersection of the two circles exist, when he shouldn't have. This, among many other things, was corrected quite recently (by Hilbert and ...
6
votes
1answer
108 views

How did the use of the word “origin” become commonplace in geometry?

My understanding is that in Cartesian geometry, all coordinate axes of an n-dimensional space may intersect at one point. I would like to know how that point--whether (0, 0), (0,0,0), ... -- came to ...
4
votes
2answers
110 views

Which is the earliest written record of hexagonal tesselation of the plane?

I am wondering which is the earliest record of the fact that the plane can be tiled by regular hexagons (in addition to triangles and squares, which may be slightly more obvious). Had a look in the ...
3
votes
3answers
132 views

When was 4D space “conceived of”?

In Measurement by Paul Lockhart (Harvard Press), he says (p.351): the classical geometers (as far as I know) never even conceived of four-dimensional space, whereas adding another variable is ...
5
votes
1answer
1k views

When Indian mathematicians learn of Euclid's Elements?

Transfer of mathematical knowledge from India to Europe (such as a positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via ...
1
vote
1answer
84 views

What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?

In modern textbooks, students are greeted with plenty of exercises. Usually they are also organized in such a way that you have examples and pointers to what concepts are most important. The elements ...
3
votes
0answers
82 views

Old geometry terminology

I was reading Ramsey's 1927 paper "A Contribution to the Theory of Taxation" and came across the following paragraph: "We have $\lambda_1 = \mu_1,\ldots,\lambda_m = \mu_m$, $m$ hyperplanes ($n-1$ ...
4
votes
1answer
89 views

Meaning of a cryptic sentence by Gauss on “the mobility of figures in the hyperbolic plane”

G. Waldo Dunnington writes in pages 189-190 of his biography of Gauss: Among the axioms of geometry which do not depend on the parallel postulate are those which secure the free mobility of a ...
2
votes
2answers
174 views

What made Euclid/Heron define line as a length without breadth and point as that with no part?

A point is that of which there is no part. And a line is a length without breadth.$^1$ If above definition on point, expresses on point as to be indivisible length, as seems to be expressed in ...
9
votes
1answer
139 views

What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this ...
4
votes
2answers
115 views

Who did the drawings in Hilbert's and Cohn-Vossen's “Anschauliche Geometrie”?

Hilbert's and Cohn-Vossen's wonderful book "Anschauliche Geometrie" ("Geometry and the Imagination") from 1932 contains a lot of great illustrations which, given the time of publication, must have ...
3
votes
1answer
134 views

How - Historically- René Descartes works affect the invention of calculus?

When "Cartesian coordinate system" been discovered By René Descartes, Algebra and Geometry become connected and vice versa , but how that exactly affect Newton and Gottfried Leibniz to invent what we ...
1
vote
2answers
297 views

Where does the word ``sine'' (as in $\sin x$) come from?

According to wikipedia (https://en.wikipedia.org/wiki/History_of_trigonometry) : the modern word "sine" is derived from the Latin word sinus, which means "bay", "bosom" or "fold" is indirectly, via ...
0
votes
0answers
87 views

Does the story about Thales and the heights of pyramids illustrate that Thales did not know of AAA triangle similarity?

Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by ...
6
votes
1answer
217 views

How did Eratosthenes determine that Alexandria and Syene were on the same meridian?

As discussed over here, Eratosthenes measured the earth’s circumference by comparing shadows cast at apparent noon at two locations separated by a known distance. Although accounts of the event (like ...
1
vote
1answer
102 views

Reference request concerning an alleged Jewish contribution to the early theory of light refraction, and to the first geometry textbook in Europe

Page 50 of the book Gustav Karpeles: A Sketch of Jewish History. Translated from the German [by an anonymous translator]. The Jewish Publication Society of America. 1897. contains the following ...
4
votes
1answer
159 views

Origin of arcminutes, arcseconds, “arcthirds,” “arcfourths,” etc

This section of a Wikipedia article says [Modern time and angle notation] contrasts with the numbers used by Hellenistic and Renaissance astronomers, who used thirds, fourths, etc. for finer ...
4
votes
2answers
149 views

Euclid’s Proposition I.3 overused?

[ Question copied from https://math.stackexchange.com/questions/2541170/euclid-s-proposition-i-3-overused ] Although the references to postulates, axioms, and previous propositions are not part of ...
0
votes
1answer
79 views

What geometric results were first proven by assuming all real numbers are rational?

Pythagoras and his followers believed that all magnitudes are commensurable; that is, the ratio of two magnitudes of the same kind, like two lengths or two areas, is equal to the ratio of natural ...
5
votes
1answer
62 views

What was the old system of using right circular cones to solve problems about circles in the plane?

[I asked this originally at the Math Stack Exchange, and they suggested I also ask about it here.] I heard about this from a college professor but haven't ever been able to find any other mention of ...
3
votes
0answers
92 views

Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
0
votes
1answer
47 views

Centroid in Babylonian Mathematics

Are there any problems in Babylonian mathematics that deal with finding the centroid of some plane figure?
4
votes
1answer
111 views

When and why was inversive geometry created/studied?

I have been revisiting math from my highschool through undergrad. I picked Courant’s excellent What is Mathematics? The flow is well so far. However, in one of the chapters he introduces inversion - ...
0
votes
3answers
190 views

What is the purpose of Gauss in his letter to János Bolyai when he mentioned “howling Boeotians”?

I'm wondering what is the purpose of Gauss in his letter to János Bolyai when he mentioned "howling Boeotians"? Is it related to some scientists or philosophers that opposed non-Euclidean geometry? I ...
-2
votes
2answers
184 views

How did the integer degrees angles counting being first adopted in geometry and mathematics? [duplicate]

The purpose of this question is trying to know originally how did counting in integer degrees angles from (one degree to $360$ degrees) being adopted basically in geometry, despite the impossibility ...
4
votes
2answers
160 views

What mathematical techniques Gauss used in order to tessellate the unit disk?

This question is a continuation of my previously posted question: Was Gauss aware of the non-euclidean implications of his work on moduler forms?, and is based on the information given in John ...
5
votes
2answers
368 views

What are the modern connections of the Pentagramma Mirificum studied by Gauss?

In the last years, i read a lot about a mathematical object that was discovered by John Napier in 1620 and explored much more deeply by Gauss, who called this "Pentagramma Mirificum" (latin for "the ...
4
votes
1answer
645 views

Sphericity of Earth from lunar eclipses - is Aristotle's argument valid?

Aristotle is often credited with proving the sphericity of Earth from the fact that the shadow of the Earth on the moon during lunar eclipses is always an arc of a round circle (as opposed to arcs of ...
2
votes
0answers
211 views

How old is the Pythagorean Theorem? [closed]

More specifically, what is the oldest evidence of human awareness of what we now call the Pythagorean Theorem? The phrase, "evidence of human awareness" was used to exclude a different question of ...
3
votes
0answers
144 views

Priority on lemniscate of Gerono?

The Lemniscate of Gerono is a special case of the Lissajous curves. The dates for the two mathematicians are fairly close: Gerono (1799-1891) and Lissajous (1822-1880). Historically who has priority ...
8
votes
1answer
248 views

Indiana Pi Bill: Other attempts to establish mathematical truth by legislative fiat?

Wiki: The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative ...
8
votes
1answer
163 views

Was a regular heptagon ever constructed by ancient Greeks?

Today it is well known that a regular heptagon cannot be constructed with straightedge and compass, since it would require to solve an equation of third degree which is not possible with the standard ...
3
votes
1answer
123 views

Straightedge and compass

According to most discussions of Euclid's Elements, this work - and indeed, much of Ancient Greek geometry - should be seen as engaged in the game of figuring out what can be done with straightedge ...
3
votes
1answer
96 views

Who was first to recognize the link between (synthetic) elliptic geometry and geometry on the sphere?

Riemann was the first to talk about elliptic geometry: Bolyai and Lobačevskij (even Gauss too) studied only hyperbolic geometry. But of course some theorems of (planar) elliptic geometry were known ...
1
vote
2answers
72 views

Whether Euclid considered squares to be rectangles

When I look up 'that which is right-angled but not equilateral' there are translations that show the word before the above phrase to 'oblong', some that show 'rectangle' and some that show both ...
7
votes
1answer
147 views

Definitions of continuity pre-Dedekind

In his article on "Kant's Theory of Geometry", Michael Friedman claims that: (...) before Dedekind mathematicians would commonly give what we call the definition of denseness when explaining what ...
2
votes
0answers
46 views

When was this projective property of an ellipse's directrix known?

I stumbled on this image from here: It's mentioned w.r.t. to the elliptical orbits of planets and how the focus-directrix property comes into play. It's an interesting POV but when was such a thing ...
5
votes
2answers
628 views

How was the focus/directrix property of conic sections discovered?

I've always thought that defining conic sections by a locus of points w.r.t the ratio of the distance to the focus and directrix was always "too artificial" - how does one actually discover this ...
1
vote
2answers
487 views

What astronomical reason led to the creation of the trigonometric sine and cosine?

Sines and cosines are commonly introduced as ratios of sides of a triangle with its hypotenuse and attributed to ancient Indian scholars. However, I've never actually thought of the reason for ...
3
votes
1answer
443 views

What is the origin of French/Burmester's curves?

French curves are a set of curvilinear rulers used in industrial design, before the advent of CAD, when everything still had to be drawn by hands. The most popular set of such rulers is made up of 3 ...
1
vote
1answer
98 views

Why is there some doubt whether or not Gauss saw the pseudosphere as the embodiment of hyperbolic geometry?

I read a lot of historical articles that doubt the possibility that Gauss saw in the pseudosphere the realization of hyperbolic geometry; that geodetic triangles on the pseudosphere obey the same ...
0
votes
3answers
2k views

How was geometry with 3 dimensions discovered/invented?

I wondered if back in the time of ancient Greeks mathematicians, 3D geometry was discovered as result of plane geometry? (Was there anything in the axioms of plane geometry that indicated existence of ...
6
votes
1answer
102 views

Has Euclid stated Cauchy's theorem?

Cauchy's Rigidity theorem says that if the corresponding faces of two convex polytopes are isometric (congruent) then the polytopes are related by a (proper or improper) motion. Cauchy's biography (...
3
votes
3answers
813 views

How did Aristotle influence Euclid?

In other words, how is Aristotle's logic represented in Euclid's Elements? I have read many articles where Euclid's Elements is linked to Aristotle's logic, but I do not understand, and I can't find ...
6
votes
3answers
272 views

What did Lobachevsky do?

It is often said that he discovered non-Euclidean geometry. But in which sense? I am reading the book 'geometry' by Brannan et al. They use the disk model as an example of hyperbolic geometry. Did ...
4
votes
2answers
269 views

What topological ideas did Gauss introduce to his student Möbius?

Recently I found a website with good historical information about the contributions of Gauss to Analysis situs (the old term for topology). The site is in German so I made a Google translate to ...