Years, Calendars and Continued Fractions - Chris Sawer
26th January 2002
Pi (the ratio of any circle's diameter to its circumference) cannot be written down exactly as a decimal or a fraction. Whenever we calculate using pi, therefore, we have to use an approximation. How can you find good fractional approximations to pi, such as 22/7 ? This presentation investigates partial fractions, which can be used to solve this problem. It also looks at how a similar idea can be applied to the number of days in a year, in order to calculate the optimum pattern for leap years. We also discover what connects Julius Caesar, Pope Gregory XIII and the French Revolution.