The Other Pure Seminar (TOPS): Continued fractions (Talk 2 of 3)

Speaker:  Sue Barwick

Title: Continued fractions

Abstract: We know that 22/7 is a good approximation for pi (with an error of  0.00126....) Why is it better than 314/100 (which has error 0.00159...)? and what is the next good rational approximation for pi? (spoiler alert, it's 333/106 with an error of 0.0000832...).

This set of talks will show that the 'best' rational approximations for irrational numbers arise from continued fractions. We will look at finite continued fractions, infinite continued fractions and periodic continued fractions and characterise them.