Questions tagged [geometry]

Branch of Mathematics about the properties of the shapes, their similarities and transformations in the space.

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How old is the idea of an Oscullating Circle? [duplicate]

In the second volume of Spivak's Comprehensive introduction to differential geometry, he begins the discussion of curvature by discussing the oscullating circle of a curve in the plane. This leads me ...
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Why did Columbus think the Earth was much smaller than it is?

Columbus set off on his westward journey to Asia, believing the Earth was much smaller than it is. There was some apparent disagreement about the size, and Columbus was staking his life on it. Why ...
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Did the ancients have the concept of dimension?

Plainly, they knew what a circle and sphere were and also a square and cube; but did they discuss the idea that a sphere was analogous to a circle but in 3 dimensions or similarly the analogy between ...
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Why 360° is assigned to circle full turn ? Not any other number? [duplicate]

Please look at this question https://math.stackexchange.com/posts/comments/9011243?noredirect=1 A user comment this so I thought of asking here You mean why did we decide on using 360 degrees? I don'...
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What is the etymology behind sine, cosine, tangent, etc.?

I heard somewhere that it was actually a mistake in translation. What's the correct story?
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What is Ptolemy holding in this picture?

I would like to know the name of the device Ptolemy is holding in the following picture. [Image Source]
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What is the origin of the "problem of Brahmagupta" of constructing inscribed quadrangle with given sides?

I am looking for a source of the following construction problem: Construct an inscribed quadrangle with given sides. I know it under the name problem of Brahmagupta, but I do not know any evidence ...
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History of points with coordinates notation

In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, ...
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Were units of area/volume always in terms of squares/cubes?

Throughout our known history of geometry were the units representing areas and volumes always in terms of squares and cubes respectively? Take ancient Egyptian formulas as an example, the fact that ...
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Historicity of Euclid. Looking for the references of Euclid in ancient texts that has survived [duplicate]

The general consensus is that Euclid was a real historical figure. Wikipedia https://en.wikipedia.org/wiki/Euclid concludes on the hypothesis that Euclid was not a real person, "This hypothesis ...
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110 views

What is the History of Coordinates?

Can someone give a history of coordinates? When did coordinates first appear, which was the first ever coordinate system? In which field were they used?
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Analysis of Moscow Mathematical Papyrus problem no. 10

This problem is giving me headaches for quite some time now I guess mainly because I am not a mathematician, but I would very much like to know if there is anyone here that has any deeper insight into ...
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How did Eratosthenes know the distance between Aswan and Alexandria?

In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
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Help understanding Egyptian circle

I was reading this Wikipedia page searching for the Egyptian area of circle and there is a following picture there: Trying to understand what is meant by this since it is under the "Area" ...
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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 ...
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Explanation of the main points in Gauss's resultant calculus

After he read Mobius's 1827 treatise on the "barycentric calculus" (according to Gauss's own testimony, he read this treatise only in 1843), Gauss wrote down several unpublished notes on ...
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Which was the first coordinate system? And why was it used?

I've been researching the motivation behind the invention of the Cartesian Co-ordinate system. But I was wondering, which coordinate system was the first to be invented? Was it the Spherical Co-...
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What does "organic" mean in old texts when describing plane curves and their construction?

I've been reading about 17th and 18th century geometers and their research into plane curves, especially algebraic curves. A term that comes up frequently is "organic". By context it seems ...
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Why is one meter as long as it is?

The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second Why is this so? Who decided that 1/299,792,458 of a ...
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Did ancient Greek mathematicians consider numbers independently of geometry?

I am currently reading Oliver Bryne's edition of Euclid's Elements, and in The Elements many arithmetic propositions are proved geometrically, and it feels to me that numbers are always treated as ...
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Platonian geometry illustrated

I recently found out that a lot of Plato's work can be drawn geometrically. See the Cerritos College YouTube video "Platos Divided Line" with the description Cerritos College Professor ...
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How did Roger Cotes come up with logarithm form of Euler formula?

I have been trying to get my head around how Roger Cotes first discovered Euler Formula. I knew how Euler did it, but I wanted a new perspective, especially from someone who discovered it earlier. ...
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Were Kepler's Laws of Planetary Motion the first formal definition of an ellipse?

It seems to me that Kepler's Laws necessitate some definition of an ellipse in terms of a coordinate system. I am wondering whether Kepler's Laws mathematically defined what an ellipse is, or if he ...
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Beltrami's Essay on the Interpretation of non-Euclidean Geometry

I am reading the Essay of the title written by Beltrami in Italian and I found a specific point of the essay which in my opinion could be fully clarified only if compared with its translations. At the ...
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Does Hadamard claim that Pascal could have discovered non-Euclidean geometry?

In The psychology of invention in the mathematical field, p. 53, Hadamard makes the following claim: Is his point that there must, in any axiomatic theory, be undefined terms, and if you write the ...
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Origin of "Inverse Pythagorean Theorem"

There is a lot of information on the history of the Pythagorean theorem, but not much on its closely related cousin; the Inverse Pythagorean Theorem. Would appreciate any resources on the the history ...
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Fourth powers and quartic equations before Descartes

How did mathematicians interpret quartic equations and fourth powers before Descartes propose to perform elementary arithmetic on line segments? I ask this because it seems strange to me that ...
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Where can I find the complete papers of abstracts published by P. G. Tait in Proc. Roy. Soc. Edinburgh in 1880?

I am interested in looking up P. G. Tait's flawed proof of the four-colour theorem, published in 1880. The citation that I have seen is: P. G. Tait, On the colouring of maps, Proc. Roy. Soc. ...
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Who came up with the name "Manhattan distance"?

Who came up with the name "Manhattan distance" (for the distance between two points as measured by the sum of the horizontal and vertical distances, as opposed to the length of the straight ...
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386 views

Historically, how did René Descartes's works affect the invention of calculus?

When the "Cartesian coordinate system" was discovered By René Descartes, Algebra and Geometry were connected. How exactly did that affect Newton and Leibniz in the invention of what we know ...
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When did Dehn start to work on Hilbert's third problem?

According to this wiki article, Dehn solved Hilbert's third problem within a year. Did Dehn start to work on the third problem after Hilbert's talk? Since Dehn is Hilbert's student, they were likely ...
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Did Galileo use an erroneous geometrical result in 'Two New Sciences'?

In Thm. 4, Prop. 4 of Galileo's 'Two New Sciences' (pg. 187, Crew Translation), Galileo says the following: "From a single point $B$ draw the planes $BA$ and $BC$, having the same length but ...
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Why is Freeth's nephroid called a nephroid?

A nephroid is an epycloid that can be generated by rolling a circle on the outside of a circle with doubled radius. It was called by Richard Proctor (1878) because its shape looks like a kidney (see ...
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What are the earliest known proofs that planimeters 'work'?

The dates of various physical implementations of planimeters are pretty well known. I'm interested in discovering when formal mathematical proofs were published that any given design does calculate ...
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How did polar coordinates come into existence?

So, I came here from Mathematics StackExchange where I posted this question. So, I want to know why polar coordinates came into existence. Why exactly did the mathematician who introduced them......
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Using Leonardo of Pisa's table of Chords

I saw a problem asking to use Leonardo's table of chords to find the arc length cut off by a chord with length 8 rods, 3 ft, and 16 2/7 unciae in a circle of diameter 10. I do not understand at all ...
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What is the basic idea behind calculation of area? [closed]

The system of calculating area in terms of square units is pretty philosophical and not very intuitive. It must have taken a great amount of time for humanity to arrive at such a convention and to ...
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When was the special relation between sides in a triangle with an angle of 60 or 120 degrees written for the first time?

The case of these triangles is special and close to the Pythagorean theorem, namely $c^2=a^2+b^2\pm ab$. This is a particular case of trigonometric relations and the law of cosines, and remains quite ...
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What is the earliest article in which Leibniz used 'matrices'?

The Chinese were using matrices ( fengcheng in the Nine Chapters of the Mathematical Art), long before they were used in Europe which suggests that possibly they were introduced by way of them. For ...
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Why couldn't Robert Peary use his theodolite at the North pole

Robert Peary writes in his book The North Pole: The instruments used in taking observations for latitude may be either a sextant and an artificial horizon, or a small theodolite. Both these ...
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What was the content of Emmy Noether's 'two-line' note on Homology?

I was surprised to learn that the note published by Emmy Noether in 1925 that suggested that Homology was better thought through as actual groups rather than numerically as Betti numbers consisted of ...
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Did physicists correct an error of mathematicians in counting twisted cubics in the quintic?

One problem in enumerative geometry consists in counting the number of rational curves of degree $d$ in the plane going through $n$ general points. If $n = 3d-1$, this number, denoted $N_d$, is finite ...
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What did Delaunay invent Delaunay triangulations for before computers were developed?

I was teaching my students about Delaunay Triangulation which is a method for dividing a surface into triangles. This triangulation method is the basis of most computer calculations that require a ...
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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 ...
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What does "given in species" mean in old geometry textbooks?

I recently came across the term "triangle given in species" in Hatton's Projective Geometry. Searching in archive.org turned up other examples (such as this) of 19th century texts, and it ...
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What was the best approximation of π known to ancient Babylonians?

Wikipedia's Babylonian mathematics says that the ancient Babylonians usually used a round value for $\pi$ (3). But they knew a more precise value: Babylonian texts usually approximated π≈3, ...
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Where in Gauss's nachlass did he pose the problem of connectedness of a surface?

On p.98 of the book "Mathematics of the 19th Century: Geometry, Analytic Function Theory", the authors mention a note written by Gauss in 1840: In 1840 Gauss wrote a note in which he introduced the ...
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How did the "Wheel of Theodorus" become known as the "Wheel of Einstein"?

I've desperately searched the Internet, to no avail, to find a citation of how the "Wheel of Theodorus" became known as the "Wheel of Einstein" as claimed by Wikipedia and Wolfram.
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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 ...
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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 (...