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 are the sources for Democritus’ experiment of dividing a shell down to its atoms?
It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits ...
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42 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 ...
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1answer
71 views
Superscripts and constants in Diophantus’ Arithmetica
Diophantus’ notation for higher powers of the unknown includes a superscript, usually written as a lowercase or uppercase upsilon - e.g., $\Delta^{\upsilon}$ as the square. It is not clear to me ...
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4answers
235 views
Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?
In the book "What Do You Care What Other People Think?", Feynman talks about how in the 16th century Niccolo Tartaglia discovered a solution to cubic equations. He says while this was not a major ...
4
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1answer
144 views
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 ...
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152 views
I can't comprehend the sentence in Euclid Elements [closed]
I am Korean, and I thought I can understand majority of english sentences, but this is really hard to translate literally for me. Even though I asked it to my English teacher, he did not know either. ...
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377 views
Why 1 was source of numbers even though ancient Greeks knew about irrational number?
In Ancient Greek, most people like Pythagoras thought 1 (monad, unity) is no number, but it is ruler and beginning of all other numbers. And Pythagoras thought everything is number. But they found ...
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65 views
On Trigonometric Methods Available to Aristarchus
Approximately 2300 years ago, Aristarchus proposed a method for determining the relative distances of the sun and the moon in relation to the earth. Specifically, he asserted that when the moon is in ...
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1answer
89 views
What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?
In modern textbooks, students are greeted with plenty of exercises. Usually they are also organized in such a way that you have examples and pointers to what concepts are most important. The elements ...
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1answer
146 views
When did people start to state and justify properties of arithmetical operations?
I have question regarding the history of the idea of founding mathematics (specially arithmetic) on a logical basis.
What I'm interested in knowing is, at what point historically people started to ...
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135 views
Does the story about Thales and the heights of pyramids illustrate that Thales did not know of AAA triangle similarity?
Thales understood similar triangles and right triangles, and what is
more, used that knowledge in practical ways. The story is told in DL
(loc. cit.) that he measured the height of the pyramids by ...
0
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1answer
105 views
What is the story behind the recently discovered gear fragment of Olbia?
Until yesterday i thought that nothing direct is known about the "Archimedes's planetarium" - an elaborate ancient planetarium based on complex gear mechanism that could represent the geocentric ...
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1answer
83 views
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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3answers
608 views
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 ...
5
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1answer
242 views
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]
...
3
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1answer
180 views
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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2answers
216 views
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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68 views
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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3answers
177 views
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, ...
3
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1answer
66 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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3answers
221 views
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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1answer
1k views
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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2answers
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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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230 views
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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89 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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1answer
111 views
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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213 views
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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1answer
190 views
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 ...
7
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1answer
555 views
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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1answer
147 views
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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1answer
88 views
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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2answers
73 views
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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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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2answers
731 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 ...
2
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2answers
344 views
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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2answers
864 views
How did Ptolemy calculate the distance to the moon?
I've read somewhere that Hipparchus measured the distance to the Moon using the lunar and solar eclipse and obtained a value of around 67.3 Earth radii. It also says that soon after Ptolemy gave a ...
3
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3answers
969 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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1answer
505 views
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 ...
5
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2answers
532 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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2answers
338 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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2answers
193 views
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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0answers
141 views
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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2answers
5k views
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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1answer
409 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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1answer
607 views
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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382 views
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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2answers
218 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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1answer
119 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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145 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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1k views
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 ...
