Fooled by Rounding

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



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.

Viewing alternatives

Download history


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions