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Questions tagged [ancient-greece]

For questions about events occurring in Greece and the immediate areas around it between 800 B.C. and 600 A.D.

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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 ...
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How was gravity explained in Ancient Greek and Roman times?

Gravity is of course something that we can all observe. Stuff falls towards the ground. But not everything: some things like steam or smoke defy this force and instead float up. During Ancient Greek ...
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Why did Euclid define “a unit” instead of “the unit”?

I know Euclid's Definition VII.1 of a unit only from English and German translations: A unit is (that) according to which each existing (thing) is said (to be) one. [translation by Fitzpatrick] ...
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Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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What was the relation between Euclid's points and Democritus' atoms?

Geometry as described in Euclid's Elements originated roughly at the same same time as Democritus described his atomic theory. I wonder how close these two points of view were related at those times: ...
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Was 360 considered a magic number, possibly?

The number $360$ as the number of units into which the circle is divided has some nice properties: it has as many divisors as a number of its size can have it's nearly the number of days per year ...
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Did Eudoxus really set out to partition irrationals (Dedekind cuts) with rationals or was that a mere side effect we perceive through our modern POV?

I've been intrigued by the similarities between what Eudoxus' Theory of Proportions and Dedekind cuts. However, I wish to question this "perceived similarity" and would like to where the flaws are, ...
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61 views

Whereabouts of oldest extant source for Apollonius’ *Conics*, Books I - IV

Regarding Conics, it is widely written, e.g. Rutger's site, that: The first four books have come down to us in the original Ancient Greek, but books V-VII are known only from an Arabic translation,...
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The Greeks did not discover “a single scientific law”

The title is drawn from a sentence in a Jim Holt article, "The Dangerous Idea of the Infinitesimal," now a chapter in his book collection.1 I found this a striking claim, and perhaps true, as the ...
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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 ...
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Did Aristotle note that ships disappear over the horizon hull-first?

I have run across several references to Aristotle's arguments for a spherical earth which claim that he noted that ships sink over horizon hull-first. For instance, Isaac Asimov writes in his essay ...
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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 ...
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80 views

Was Aristotle first to talk about gravity?

Aristotle was chatting about forces we later identified as gravity at about 300BC. He made a few mistakes regarding heavy objects falling faster etc, but that is by the by. Was he the first ever to ...
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What field will we be remembered for developing? [closed]

I had a course on History of Mathematics this semester and it seemed that each civilization became known for developing a particular area of mathematics. For example, Arithmetic and Ancient Egypt/...
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How was the Antikythera Mechanism moved?

I understood all the gears and cogwheels in the Antikythera Machine, but I not sure what make all these stuffs works inside the box. It's mechanical movement done by hand-wound style?
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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 ...
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Did Indian astronomers realize the sphericity of the earth independently of the Greeks?

Reading Wikipedia's articles on the flat earth, spherical earth, and history of geodesy makes it clear that virtually every society recognizing the spheroidal shape of the earth today owes the ...
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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 ...
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What did the Greeks call the “trial and error” reasoning process?

What did the Greeks call the "trial and error" reasoning process? Bruce Aune's review of Wilson's Peirce's Empiricism: Its Roots and Its Originality claims "The name 'empirici' is in fact traceable ...
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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 ...
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466 views

Compass and straightedge: why?

Why is it that, in ancient Greece, mathematicians tried to solve geometrical problems using compass and straightedge only and, apparently, only if that failed, they tried to use other tools? Note that ...
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367 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 ...
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Was Babylonian Mathematics as sophisticated as Greek mathematics?

Why its true that the Egyptians did not see much developments. It has been said that the Babylonians were equal to the Greeks in mathematical achievement in terms of having an axiomatic, deductive ...
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How did Ptolemy calculate the distance to the moon

I've read that Hipparchus measured the distance to the Moon using the lunar and solar eclipse and obtained a value around 67.3 Earth radii. It also says that soon after Ptolemy gave a more accurate ...
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472 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 ...
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What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
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204 views

how sophisticated was Egyptian and Babylonian mathematics compared to the Greeks

It seems like the focus always tends to be on the achievement of Greek math (which strikes of eurocentrism a little bit) while civilizations like the Egyptians and Babylonians are overlooked why do ...
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247 views

When $1$ wasn't really a number in Greece

I'm reading "Professor Stewart's Incredible Numbers," by Ian Stewart and in there it is claimed that In early Greece, the list of numbers started $2, 3, 4,$ and so on: $1$ was special, not "really" ...
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How did Archimedes arrive at his principle in his time?

Archimedes principle: Any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. I get that this can be ...
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Plato's chemical formula for water

In a paper about Plato's Timaeus I came across a cryptic note saying: "Academic research usually avoids noting that Plato's assertion about water consisting of two parts air and one part fire is ...
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Did the ancient Greeks have zero in their number system?

Roman numerals don't have 0. I was taught that the arabs introduced 0 in their arabic numerals and it is depicted as a decimal point. The arabs, in turn, got their number system from india in ...
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169 views

Instances of the use and application of mathematics in Ancient Greece

I am setting out to write a paper, the thesis of which only needs to have the property that it addresses "how was mathematics used in Ancient Greece". I have begun my own investigation (i.e. ...
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What is the history of angle quintisection (division into five equal parts)?

I was reading lately that the quintisection of an angle is possible with paper folding (origami). Now, in contrast to the trisection of an angle, a problem which was discussed historically, and was ...
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What did ancient near eastern protoscience believe about germination?

Two Bible verses seem to indicate that ancients believed germination was the death of a seed, and a resurrection or rebirth of that seed into a plant: Unless a grain of wheat falls into the earth ...
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205 views

Looking for source of foods associated with specific humors

Let's get this out of the way- I am aware that this is nonsense today. However, historically it would have been considered science, so I'm asking here rather than in the History SE. Classically, ...
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114 views

Which ancient mathematician was opposed to “application” of math?

I seem to recall reading about a mathematician from antiquity whose view was, roughly, that to "apply" math was to do it violence (or indeed, to expedite violence) and so looked down on applications. ...
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135 views

What manuscript is depicted in the HSM advertisement?

The following advertisement recently appeared in the sidebar on math.se: Is the Greek script on the left actually from a mathematical manuscript? What is its source?
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Why wasn't probability developed in ancient Greece?

The modern axiomatic approach to probability was established by Kolmogorov nearly 70 years ago. According to Wikipedia, the first ideas connected to a mathematical theory of probability arose with ...
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What are the earliest mentions of Prime Numbers?

Egyptians and Babylonians must have had some ideas about primes but what are the earliest mentions or comments? Where is the first list of primes? After Burkert's work on Pythagoreanism an answer ...
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Why does Aristotle write 'astrology' when Plato writes 'astronomy'?

Checking modern quotes from Aristotle almost everywhere the word astronomy is found to be replacing the original Greek or Latin astrology' (astrologia). In Plato'...
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When and who was the first mathematicians to prove rigorously that $\sqrt[3]{2}$ was impossible number? [closed]

The purpose of the question is to understand why the number $\sqrt[3]{2}$, that was proven rigorously by ancient Greek is an impossible number (even at infinity), by their three famous impossibility ...
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675 views

Who discovered integer triangles with one angle trisecting another?

When & who was the first mathematician to discover the following simple triangle with a unique property that it has one angle is equal to one third of another angle in the same triangle? The ...
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Did the Greeks discover the irrational numbers? [duplicate]

My history of maths lecturer claims the Greeks did not discover the irrational numbers. Is this true?
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Did Pythagoras exist? [duplicate]

My history of maths lecturer claims Pythagoras never existed. Is this true? Is there any evidence he existed? He also claims the Pythagoreans did not discover or prove the Pythagorean theorem.
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573 views

How did Archimedes's water clock work?

I read that several principles of Al-Jazari's monumental water clocks were based upon earlier designs of water clocks by Archimedes, for example the use of valves, feedback system and flow control ...
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818 views

The origin of quadratic equation in actual practice

I read that in ancient times the quadratic equation of this kind $$x^2+10x=39$$ had been solved long ago. I read that this kind of equation originated in the geometric question of "Given an area of 39,...
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What are Archimedes's contributions to the principle of the screw pump?

I read that the famous screw pumps were used before Archimedes (in the hanging gardens of Babylon for example), and that the Archimedean screw is named after him because he "developed a rigorous ...
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Is there any historical “evidence” maintaining that Euclid is a single person?

Bourbaki, for example, is 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 ...
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Did Archimedes know about Callipus?

Various sources, such as Cicero's Republic state that Archimedes had made a machine consisting of glass spheres that represented the Eudoxian system of the world. Considering that Callipus died over ...
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Plane/composite numbers as lines?

In the Elements of Euclid a plane number (i.e. a composite number), was represented by a line AB. But, being a plane number a multiplication of two numbers (i.e. two lines, in the mind of a ...