# Questions tagged [geometry]

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

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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?
647 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 ...
3k views

### Who was the first to calculate $\pi$?

I am very interested in the history of $\pi$. I am first trying to find out who calculated it. Many sources have different answers, from the ancient Egyptians, to Archimedes, to the Babylonians. I ...
3k views

### How was Newton's classification of cubic curves completed?

According to what I have read, using Newton’s methods there are 78 different families of cubic curves. Newton discovered 72 of them while “subsequent research identified another 6”. This paper ...
646 views

### What made Euclid/Heron define line as a length without breadth and point as that which has 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 ...
592 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 ...
362 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 ...
567 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 ...
1k views

### First proof that circumference/diameter $=\pi$

I am interested in this question: Who was the first to show that for every circle the fraction $$\frac{\text{circumference}}{\text{diameter}}$$ is always constant? I am not interested in $\pi$ ...
244 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 ...
1k 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 ...
425 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 ...
2k views

### How did Eratosthenes knew the exact time of the day?

Eratosthenes measured the radius of the Earth with an incredibly accuracy. To do it, you need to measure the length of the shadows from 2 different cities at the same time of the day. Then knowing ...
351 views

### What were Riemann's other two submissions for his habilitation?

In Stalking the Riemann Hypothesis, Rockmore discusses how Bernhard Riemann, as per custom, submitted three potential areas of research for his habilitation. Gauss was the chairman of the committee ...