A question on simplifying continued fractions, and the number theory.?

Question

Hey, I'm doing a geometry project that's due in a few days, and i'm starting early because I'm not finding much online. I am doing a report in Aida Yasuaki, a famous Japanese mathematician. He is noted for his work on the number theory, simplifying continued fractions, and so forth. I have to make a poster board with some facts about him...I need help because I don't know much about the number theory or fractions, and I'm in the 10th grade !

the bottom line:

*I need a definition of the number theory, and an example I can write on the poster board
*AND I need to know the definition of a simplified continuing fraction, and I'd like an example of a simplified continuing fraction problem that I can write on my poster board

:) thank you all so much, you've helped me on previous projects, and things always go well ! :)

Answer 1

Number theory is a branch of mathematics. It is not *the* number theory. Anyway, number theory is the investigation of the properties of whole numbers (integers).. It tends to consider aspects of divisibility, prime factorization, etc.



Continued fractions are a bit harder to describe in this forum. They are closely related to best rational approximations as well as certain questions in number theory. In particular, they are very important for studying Pell's equation:

x^2-n*y^2=+-1.

It turns out that the continued fraction expansion of the sqare root of n ican give solutions to this equation in integers.

Answer 2

by grinding out the respond with a calculator, commencing with an 10-digit representation of ?2 you will get an answer for a) that has the persevered fraction section repeating a million and four alternately and curiously indefinitely. an identical component happens in b) using ?11 and in c) root 5 degenerates to a string of four's ?5 = < 2; 4, 4, 4,....> That leads me to think of there could desire to be an analytic answer. yet I have no wisdom of the deeper concept of persevered fractions and perhaps you're meant to grind the solutions out like this :-(

Answer 3

Continued fractions :



http://mathworld.wolfram.com/ContinuedFraction.html

Answer 4

how are you starting early if its due in a few days?!