15
votes
5answers
566 views

Historical use of figures in geometry

I was surprised to learn from John Stillwell's comment in answer to the question, "Can the unsolvability of quintics be seen in the geometry of the icosahedron?", that There is not a single ...
2
votes
2answers
535 views

Has the notion of “space” been reconsidered in 20th century?

The original title, "has the bases of geometry been reconsidered in 20th century" of this question refers to Riemann's paper "On the Hypotheses which lie at the Bases of Geometry", an English version ...
5
votes
2answers
762 views

Original proof of Pappus' Hexagon Theorem

Does anyone know where I can find an english translation, preferrably online or in a book the library of a small liberal arts college would be likely to have, of the original proof of Pappus' hexagon ...
4
votes
1answer
754 views

What is the origin of unit vector notation? (i,j,k)

What is the origin of this notation? Who coined them and for what purpose?
13
votes
1answer
2k views

Ping-pong relief map of a given function $z=f(x,y)$

I have an idea to design a type of Galton's Board to "draw" a relief map of a given two-dimensional function $z=f(x,y)$. A typical Galton's Board drops, say, ping-pong balls through a series of evenly ...
0
votes
0answers
340 views

Current validity for Erlangen in some or other form?

I’m referring, naturally, to Felix Klein and his Erlanger Programm (http://en.wikipedia.org/wiki/Erlangen_program). Colloquially put, “groups rule geometry OK”. To be more sophisticated about it, ...
27
votes
10answers
3k views

Is there a mathematical axiomatization of time (other than, perhaps, entropy)?

Since Euclid's axiomatization of space, we have developed a sophisticated mathematical model of space. Given a category of structures (measures), local space is modeled the spectrum of measurements ...
1
vote
1answer
355 views

English translation of Lambert's Theorie der Parallellinien?

Does anyone know if there is an available (published or unpublished) English translation of Johann Lambert's Theorie der Parallellinien? I was able to find it online in German by way of the ...
4
votes
2answers
765 views

Is there any documented study of geometry in contemporary primates ? [closed]

There are many studies of language learning abilities of primates (mostly chimpanzee, bonobo) and studies of tool use, knowledge transmission and number sense. Are there studies or documented cases ...
5
votes
1answer
817 views

Did Apollonius invent co-ordinate geometry?

When I read descriptions of Apollonius' treatise on conics, some of them say that he invented co-ordinate geometry, some say that he kind of did and others are silent on the matter. Or is it the case ...
4
votes
4answers
2k views

completeness axiom for the real numbers

Do any treatises on real analysis take the following as the basic completeness axiom for the reals? "Let $A$ and $B$ be set of real numbers such that (a) every real number is either in $A$ or in $B$; ...