Benjamin Banneker's Inscribed Equilateral Triangle

Editor’s note: This article was published in May 2005.

Benjamin Banneker, the son of a former slave, was born in 1731 on a farm near Baltimore. From books loaned by a neighbor, Banneker taught himself surveying, astronomy, and mathematics. He later published several almanacs containing his astronomical observations. These almanacs widely distributed in Pennsylvania, Delaware, Maryland and Virginia. In 1791, Banneker received an appointment to assist in the survey of the boundaries of the Federal Territory - a ten-mile square now known as the District of Columbia. Banneker was also a social activist; he wrote a long letter to Secretary of State Thomas Jefferson likening the slavery of Negroes in the US to the enslavement of the American Colonies by the British. He attached his first Almanac as evidence that an African-American could be a distinguished scientist. Banneker died in 1806 on his Maryland farm. Banneker was honored on a 1980 US postage stamp.

In his journals, Banneker wrote and collected mathematical puzzles written in verse. These journals served as his notebooks for astronomical observations, his diary, and his math notebook. Unfortunately only one of his journals survived a fire on the day of his funeral. The mathematics in this journal consisted of six puzzles and two pages of mathematical writing. Banneker's six puzzles from the journal were published in an excellent biography of him written by Silvio Bedini. To my knowledge, much of Banneker's mathematics in his own handwriting has never been reproduced. I located a microfilmed copy of his journal at the Maryland Historical Society in Baltimore. The quality of the reproduction was poor, but I was helped by Mr. Omar Rumi of Kuala Lumpur, Malaysia, and my son, Quinn, a student at MIT. With the combination of Banneker's excellent penmanship, quality scanning and most of all painstakingly accurate photographic retouching on the part of Mr. Rumi, I am able to reproduce Banneker's actual handwriting of his mathematics.