Fooled by Rounding

Mason, John and Zazkis, Rina (2019). Fooled by Rounding. Digital Experiences in Mathematics Education, 5(3) pp. 252–265.

DOI: https://doi.org/10.1007/s40751-019-00055-2

Abstract

For any convex quadrilateral, joining each vertex to the mid-point of the next-but-one edge in a clockwise direction produces an inner quadrilateral (as does doing so in a counter-clockwise direction). In many cases, a dynamic geometry measurement of the ratio of the area of the outer quadrilateral to the area of the inner one appears to be 5:1. It turns out, however, that this is due to rounding. We generalise the construction by replacing mid-points by more general ratios, finding the maximum and minimum values of the area ratio and determining the conditions on the original quadrilateral that achieve those two extremes.

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