You are here:
Number Theory/pi
Advertisement
Question
Hello Vijilant,
1.Why pi is an irrational number, since pi=circumference/diameter(If both circumference and diameter are integers, then pi will become rational? isn't it? But, I studied, pi cannot be written as ratios. What's going on here? Please explain me.
Hello Shameem
Every proof that PI is irrational is difficult and demands at least a very good understanding of analysis. See for instance http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
Of course both the circumference and diameter of a circle cannot be integers. This is just another way of saying PI is irrational.
Best wishes
vijilant
Related Articles
Vijilant
Expertise
Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.
Experience
Teacher of math for 50 years
Organizations
ATL
Publications
Journal of mathematics and its applications
Education/Credentials
BSc Hons Liverpool
Awards and Honors
State Scholarship 1955
Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things.
One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.
©2012 About.com, a part of The New York Times Company. All rights reserved.