Of Art & Math

Of Art & Math is a series of articles published in At Right Angles, a mathematics education magazine. These articles – written by Punya Mishra and Gaurav Bhatnagar – are meant to introduce readers to the fascinating connection between art and mathematics through visual wordplay.

The articles (along with brief descriptions) are found below. Click on the headings below to open up each article PDF in a new window.

1. Introducing Ambigrams

ambigram-standard-rotational
Ambigram for the word “Ambigram”

Mathematicians love puzzles—they love to play with numbers and shapes but often their love can turn to words and other areas that, at least on the surface, have little to do with mathematics. One form of visual wordplay with some deep connections to mathematics are called ambigrams.  Ambigrams exploit how words are written and bring together the mathematics of symmetry, the elegance of typography and the psychology of visual perception to create surprising, artistic designs.

2. Symmetry

invariant
Ambigram for the word “invariant” showing rotational symmetry

Symmetry is all around us. Symmetry can be seen in regularities of form found in the natural world. A face is symmetric as is a butterfly. When mathematicians say an object is symmetric they mean there is a transformation that moves individual pieces of the object but does not change the overall shape. Mathematicians have identified 4 key transformations, namely, rotation, reflection, translation and scaling. As you will see and read in this article, ambigrams often play with many of these transformations – either taken one at a time or in groups.

3. Self-Similarity

similarity
Ambigram for Similarity

Self-similarity in geometry is the idea of repeating a similar shape (often at a different scale) over and over again. In other words, a self-similar image contains copies of itself at smaller and smaller scales. Self-similarity is a rich mathematical idea and connects to other powerful concepts such as infinity, iteration, fractals, recursion and so on. As it turns out self-similarity is also a rich source of ambigrams as you will see in this article.

4. Palindromes

racecar-palindromeANDambigram
A word that is both a palindrome and an ambigram

Palindromes are words (or numbers) that read the same backwards and forwards. There is a certain surface similarity between palindromes and ambigrams—though some key differences as well. In this article, we explore the idea of palindromes through a pretty unique perspective. Note: This is a pre-publication version of the article

5. Paradoxes I

paradox
Rotational ambigram for the word “Paradox”

From self-reference to circular proofs, from thoughts on the nature of mathematics to Zeno’s Paradox—this article has them all. Note: This is a pre-publication version of the article

6. Paradoxes II

penrose
An impossible object also known as a Penrose Triangle 

Continuing the exploration of paradoxes, this article delves into ideas of self-reference, specifically as seen in Russell’s paradox and the liar paradox. It ends with an exploration of visual paradoxes and the nature of mathematics. Note: This is a pre-publication version of the article