# Questions tagged [geometry]

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

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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 ...
92 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?
183 views

### 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 ...
49 views

### 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" ...
115 views

### 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calculus" (according to Gauss's own testimony, he read this treatise only in 1843), Gauss wrote down several unpublished notes on ...
42 views

### 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-...
261 views

### 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 ...
3k views

### 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 ...
54 views

### 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 ...
64 views

### 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 ...
85 views

### 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 ...
90 views

### 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 ...
100 views

### 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. ...
150 views

### 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 ...
147 views

### 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 ...
127 views

### 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 ...
233 views

### 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......
63 views

### 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 ...
82 views

### What geometry is involved in the architecture of Indian stupas?

Is there any interesting geometry involved in the construction of Indian stupas such as the Great Stupa at Sanchi? There are interesting geometric patterns in the architecture of Stonehendge, ...
108 views

### 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 ...
90 views

### 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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### 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 ...
72 views

### 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 ...
148 views

### 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 ...
142 views

### 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 ...
143 views

### 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 ...
467 views

### 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 ...
194 views

### 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.
108 views

### 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 ...
111 views

### 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, ...
126 views

### Lessons from apparent paradoxes in geometric limits

1) Zeno's oxymoronic fleet, stationary arrow: One of the earliest infinity paradoxes, of course, is the flying arrow of Zeno which can't possibly be moving since it takes a finite amount of time to ...
216 views

### What mathematics did Isaac Newton learn at school?

Since Sir Issac Newton invented a lot of modern mathematics, what mathematics did he already know? Since he was standing on the shoulders of giants which giants was he speaking of? I presume he knew ...
85 views

### Literature on Mayan mathematics

I asked this question on math.se and they sent me here. It is well known that Mayan people used vigesimal (base 20) numeral system, and had had an advanced calendar system. Except for these facts, I'...
82 views

### Who invented the push-pull construction?

I learned about the push-pull construction from a video lecture by Freedman in which it is explained starting around 39:08. It is somewhat long and technical to describe in detail, but the main idea ...
163 views

### Were epicycloids from astronomy acceptable curves in Greek geometry?

My simplified historical understanding is as follows. Euclidean geometry accepted a limited number of geometrical objects (straight-edge and compass constructions, conics). Descartes' Géométrie ...
331 views

### 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 ...
396 views

### 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 ...
143 views

### Did Newton invent convex hulls?

The convex hull of a set of points appears recognizably in a 1676 letter from Newton to Henry Oldenburg describing Newton polygons. Is there an earlier precedent for convex hulls or is this their ...
97 views

### What are the context and motivation for Gauss's study of the "Pothenot problem"?

My question refers to p.307-335 of volume 8 of Gauss's werke, which are part of a section of volume 8 which deals with Gauss's applications of complex numbers for geometry. The pages mentioned are ...
129 views

### 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 ...
556 views

### What is the history of staircase or 𝜋=4 paradox?

The staircase 'paradox' has been discussed here and elsewhere a few times (search for staircase + paradox). My question is whether this puzzle has been discussed in the academic literature or ...
112 views

### When did the use of Sine and Cosine as functions become mainstream?

In the work of early physicists like Newton, everything is explained in terms of cumbersome (in today's standards) geometry. They don't talk about "cosines" of certain angle, but about proportions ...
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### 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?
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### 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 ...
203 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 ...