In this part we will concentrate on another infinite two-dimensional pattern called the wallpaper pattern and also explore aspects of symmetry in the everyday objects around us. For ease, we reiterate the ‘working definition’ of symmetry here. (the 1st part)

Many of the inanimate objects around you probably seem perfectly still. But look deep into the atomic structure of any of them, and you’ll see a world in constant flux — with stretching, contracting, springing, jittering, drifting atoms everywhere. Ran Tivony describes how and why molecular movement occurs and investigates if it might ever stop.

Symmetry seems to be very much a part of our genetic make-up. Even a young child, unschooled in matters, is able to differentiate between symmetrical or regular objects as compared with those that are irregular. Our hearing is tuned to recognise symmetry in rhythm, music and beats. We see beauty in symmetry of monuments, designs, decorations and art. The aim of this article is two-fold. The first is to introduce the reader to the intuitive as well as the mathematical concept of symmetry.

In this article, we return to Viviani's theorem and discuss a proof-without-words.

Pentomino puzzles are a valuable educational resource in their avatar as puzzles, they can also be used effectively to build spatial intuition.

Here is a resource on multilingualism that can be used in the process of developing language sensitivity and communicative competence.

In our November column we introduced the concept of ambigrams—the art of writing words in surprisingly symmetrical ways. In this column, we use ambigrams to demonstrate (and play with) mathematical ideas relating to symmetry and invariance.

A nice investigation with dynamic geometry for students at high school is the so-called Midpoint Trapezium theorem...
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