greek matematicians?

Question

I was told by my math teacher that there were 2 greek matematicians that found an easy way to solve an equation with 2 variables, with the assumption that all the variables are whole numbers. Does anyone know their names, or anything about it??

Answer 1

Euclid and Diophantus

The linear Diophantine equation ay+bx =1 (where a and b are relitively prime) can be solved by using the extended euclidean algorithm.

For example
3x+ 5y = 1
Apply euclidean algorithm (calculate gcd(5,3))
5 = 1*3 + 2
3 = 1*2 + 1
Rearange the equations to,
1 = 3 - 1*2
2 = 5 - 1*3
Now combine,
1 = 3 - 1*2
1 = 3 - 1*(5 - 1*3)
1 = (-2)3 + (1)5
hence x=-2 and y=1

Answer 2

Diophantos of Alexandria (c. 250 A.D.) is the Greek whose name is associated with whole-number problems of many different kinds. His other work is mostly ignored, and no other Greek comes anywhere near him in reputation for working with such problems, so much so that equations requiring whole-number solutions are still called "Diophantine Equations".

The Greek mathematician Euclid (c. 300 B.C.) is better known for geometry, but he also did some important basic work on whole numbers. One of his algorithms (Euclid's Algorithm for the greatest common divisor of two numbers) turns out to be an ideal tool for constructing the solution of a linear equation in 2 variables which have to be whole numbers, but that's not what he invented it for, and Diophantos never bothered with such simple equations - his stuff was far more complicated!

Well, two famous Greeks, but no clear answer to your question, sorry.

Answer 3

I would guess that one is Archimedes. He was one of Ancient Greece's mathematicians. He calculated the value of pi (in fraction form; they didn't have decimals), and invented a ton of stuff.

As far as what you're talking about, I don't know.

Answer 4

Archimedes and Pythagoram.

Or maybe Hercules and Onyerknees

Addalottastuff and Divideathon???

Answer 5

i think that long before anyone did, indian mathematicians discovered much more in mathematics... including solving complex equations, use of zero, continued fractions etc

have a search on 'vedic mathematics'

one site: http://vedmaths.tripod.com/sseq/index.htm

also see: http://www-groups.dcs.st-and.ac.uk/~history/Timelines/TimelineA.html

Answer 6

no but i'm greek, megale!