Friday, December 20, 2002

Experience Mathematics #23 -- Ambigrams (by Punya Mishra)

Symmetry is important in mathematics and in art. Today we will look at a special kind of wordplay based on ideas of symmetry and figure and ground. Consider the word below: 

Can you read it? Now turn the page you are holding upside down and try reading it that way. The word stays the same. This image/word has rotational symmetry—essentially, it stays the same when rotated 1800.

Such visual wordplays are called ambigrams. The word “ambigram” was first coined by the cognitive scientist Douglas Hofstadter. Here is an ambigram of the word ambigram itself.

Ambigrams can be of many different kinds. For instance consider the word “logical” below.

This word has reflection symmetry i.e. it will read the same even when reflected in a mirror.

Some ambigrams are not about symmetry as much as they are about reading words in multiple ways. Here is one titled “good-evil” Can you see both words? Look carefully. This is similar to figure-ground paintings by M. C. Escher.

Creating ambigrams is great fun. Why don’t you try creating some yourself? If you want to see more examples of such wordplay you can search on Google or go to my wordplay gallery:

This guest column has been written by Professor Punya Mishra, College of Education, Michigan State University, USA. You can email him at

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