Fooled by Rounding

Journal article

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.

Authors: Mason, J; Zazkis, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Digital Experiences in Mathematics Education
• Volume: 5
• Issue: 3
• Pages: 252-265
• Publication date: 2019-10-08
• DOI: 10.1007/s40751-019-00055-2
• EISSN: 2199-3254
• ISSN: 2199-3246
• Language: English
• Keywords: Geometry-algebra interplay; Convex quadrilaterals; Being misled by missing decimal places; Dynamic geometry software; Ratios of areas; Computer algebra software