History of i,j,k variables

Matt Chung

Oct 29, 2018

Any time you read code (in production or from a textbook), you’ll often see the control variable, when employing for loops, being declared with the variables i,j,k. And for most of my programming career, I’ve never really questioned why we specifically choose those three letters. Why not m (a great letter), or c or d or e — or any other letter for that matter. Seems rather arbitrary.

But, I suspect that it has to do with William Rowan Hamilton, a famous Irish mathematician, who published a book in the 1800’s, the book titled “A theory of Systems of Rays”. And in this book, William uses i, j, k notation when representing vectors (in R3). This representation of vectors became the standard notation and he’s the person we need to thank when we type in those three letters when programming.