In this episode of "How To Prove It", we discuss some more applications of Ptolemy's theorem.

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.

Expose your learners to 'degenerate' triangles.

These are excellent GeoGebra exercises for students helping them to develop and practise skills of visualisation, logical sequencing, making connections and recalling theory. Read on.

Revisit the way you can bisect an angle, with a fresh twist.

Take the perennial favourite Pythagoras theorem to the classroom and pose these investigative questions. Spiral of square roots perks up the proceedings!

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.

Here's an addendum to Fagnano's Problem.


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