When is a square a triangle?

Summary

The number 36 has the remarkable property that it is both square and triangular, since it equals 6x6 and 1+2+3+...+8. That is, a 6x6 array of dots can be perfectly rearranged into a triangular stack with 8 dots on the bottom row. Apart from the trivial case of the number 1, which is regarded as both square and triangular by convention, are there any other numbers with this property? It turns out that this talk on geometric properties of whole numbers is really about fractions, quadratic equations, surds, approximation, sequences and matrices, with a few passing references to calculus and algorithms thrown in for good measure. Links will be made between these concepts from the Australian Curriculum and key ideas from the ANU Extension course for Year 11/12 students and the Australian Maths Trust’s Olympiad program.

Presenters
Chris Wetherell

Session Code Session Date Session Start Session Finish Session Location Places Remaining
E-06 05/12/2019 03:40 pm 04:40 pm La Trobe University, Bundoora
29

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