December 1, 2021
Speaker: Scott Farrand
Title: Reenvisioning Rational Numbers
Hover over for abstract
Rational numbers are commonly conceived of as quotients of integers, or as repeating decimals, and occasionally as continued fractions.
We will explore a novel way of viewing rational numbers (seriously, a completely different way of describing a fraction),
which then begs us to explore how various aspects of fractions and elementary number theory are reflected in this view, with fascinating results.
We'll also extend this perspective on rational numbers to include real numbers, finding use for a bit of classical number theory to view a quadratic surd.
The opportunity to explore a mathematical realm that is new to us all, yet yields to our intuition and exploration, is an excellent chance to think about how we approach what we seek in mathematics.