Questions tagged [euclid]

Euclid of Alexandria was a Greek mathematician and the "father of geometry".

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What is the origin of "two straight lines cannot enclose a space" axiom in Euclid's Elements?

This post is prompted by a recent question on MSE asking about "Axiom 10" of Euclid's Elements, as found in editions by Byrne and Conway: "Two right lines cannot enclose a space". ...
RobinSparrow's user avatar
0 votes
1 answer
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Euclid's use of antenaresis and Heath's commentary

In Book 7, Prop. 1. Euclid uses repeated subtraction to prove that two numbers are relatively prime. As explained here the Greek word for repeated subtraction is "antenaresis". There isn't ...
zeynel's user avatar
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1 answer
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The role of the Elements in the development of mathematics

The Elements are often regarded as the cornerstone of the axiomatic approach to mathematics. However, mathematical textbooks have served as the foundational pillars upon which writing style, language, ...
Leandro Caniglia's user avatar
3 votes
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Who came up with the proof of "Bézout's identity" that uses the well-ordering principle?

Let $a$ and $b$ be two integers not both of which are equal to zero. It is an important and well-known fact that $\text{gcd}(a,b)=ax_{0}+by_{0}$ for some integers $x_{0}$ and $y_{0}$. Even though this ...
José Hdz. Stgo.'s user avatar
4 votes
1 answer
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Who first proved necessity of Euclid's formula for pythagorean triples?

The following well-known formula for pythagorean triples is commonly called Euclid's formula: If $a, b, c$ are three natural numbers with $a,c$ odd, $b$ even, $\gcd(a,b,c)=1$ and $a^2+b^2=c^2$, then ...
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History of greater-than symbol used in reverse?

I was surprised to find that Oliver Byrne's 1847 marvelous The Elements of Euclid (color version)1 uses $\sqsubset$ to mean "greater than" and $\sqsupset$ to mean "less than," in ...
Joseph O'Rourke's user avatar
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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 ...
Biswarup's user avatar
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2 answers
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What happened to the original sources of Euclid's Elements?

I am aware of the fact that Euclid's Elements is a compilation of the works of previous Greek mathematicians like Thales, Pythagoras (his school), Eudoxus, Theaetetus, etc. However, I want to know the ...
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16 votes
2 answers
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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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Euler's proof of infinite primes first since Euclid?

Q. Is it true that Euler's proof of infinite primes was the first since Euclid's which was from around 300BC? Note: By Euler's proof, I mean the use of his Euler product formula for the zeta function ...
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Are Euclid's theorems and proofs due to Euclid?

Some appear to argue that much of the Elements by Euclid is a compilation of knowledge handed down to Euclid from his predecessors. On the other hand, some credit the proof, of the Pythagorean theorem ...
Chris Judge's user avatar
6 votes
1 answer
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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 (...
Alexandre Eremenko's user avatar
5 votes
3 answers
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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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Is there any historical "evidence" maintaining that Euclid was a single person?

Bourbaki, for example, was the name of a set of mathematicians, rather than a single person, under which several books were published. Out of curiosity, I wonder if there is any historical evidence ...
Yes's user avatar
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2 answers
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When did the people start using the portraits of the two Euclids interchangeably?

According to the folks of Wikipedia, this is the portrait of Euclid of Alexandria (the "Father of Geometry"): Yet, I read several years ago on MathOverflow that the individual in the ...
José Hdz. Stgo.'s user avatar