This article is the first in a series dealing with inequalities. We shall show that in the world of algebra as well as the worlds of geometry and trigonometry, there are numerous inequalities of interest which can be proved in ways that are easy as well as instructive.
Mathematical investigations are perfect for Low Floor High Ceiling activities. Here, we have described how a simple pattern can be recognized, investigated, played with and generalized. If your students have enjoyed DADS Rule, do let them try the same strategies with other number patterns; we hope they rule!
A Kepler triangle is a right-angled triangle whose sides are in Geometric Progression, which requires that its sides are in the ratio 1 : √ φ : φ where φ = ( 1 + √5 )/ 2 is the Golden Ratio. Here is an unexpected demonstration of the Golden Ratio.