by Professor M.E.
In the last lecture
of the Science College Public lecture series for 2000/2001, Professor
Roger Cooke, of the University of Vermont, lectured on Brahmagupta,
Pythagoras, and Fibonacci to an appreciative audience.
Cooke mesmerized more than 500 students, professors and members of the
general public with his fascinating account of the beauty, complexity,
and relevance of numbers and patterns of numbers to the real world. He
spoke of the tensions between discrete and continuous mathematics, and
illustrated them with historical anecdotes about how the processes of
counting and measuring have spawned very different kinds of mathematics.
By considering such concrete problems as determining the cost of filling
up a fuel tank, Cooke led the audience step by step to the distinction
between integers and real numbers. He explained how integers are the basis
of arithmetic, real numbers the basis of geometry.
Money belongs to arithmetic, areas and volumes to geometry. Yet the two
are frequently linked by commercial transactions such as calculating the
cost of filling up a fuel tank.
Professor Cooke explored the difficulties involved in such tasks as measuring
the speed of light and determining the circumference of a circle, and
showed why some of these tasks require the idea of infinite precision.
He pointed out that one of the challenges of the world of digital computers
is how problems involving infinite precision can be solved with tools
that are inherently finite.
In his excursions into the history of mathematics, Cooke explained the
connections between the work of Brahmagupta, Pythagoras, and Fibonacci.
He showed how the seventh-century Hindu mathematician Brahmagupta solved
problems involving the measurement of time by applying the algorithm for
finding the greatest common divisor of two integers.
The talk ended with a vivid and concrete illustration of how the Fibonacci
series of integers can be used to explain in mathematical terms how sunflower
seeds appear to grow in graceful interwoven spirals.