
06546551
j
2016b.00582
Pritchard, Chris
The problem with square pegs and P\'olya's lesson on how to solve it.
Math. Sch. (Leicester) 40, No. 3, 1619 (2011).
2011
Mathematical Association (MA), Leicester
EN
G40
G60
plane geometry
triangles
squares
area
ratio
proportion
trigonometry
regular polygons
P\'olya
optimization
extreme value problems
ME 2016b.00574
From the text: This is the fourth in a series of articles prompted by thoughts about what proportion of the area of a figure is taken up by a common shape drawn inside it. Each article has made use of mathematics available to high school pupils in their middle to senior years. The mathematics associated with inscribing squares in polygons and sectors is equally accessible. It is inspired by one of the exercises in heuristics set by Georg P\'olya (18871985). For the previous Part see [the author, ibid 40, No. 2, 1215 (2011; ME 2016b.00574)].