Monday Morning Math: Omar Khayyam


Good morning!  Our mathematician today is Omar Khayyam.

Omar/Umar Khayyam was born in Nishapur, Persia, (modern day Iran) in 1048. Not much is known about his mother, but his father was a doctor who hired tutors to teach Omar.   Omar Khayyam is known for his mathematics, including writing down the laws of algebra that we know today.  He was able to make progress toward finding a general formula for ax^3+bx^2+cx+d=0 similar to the quadratic formula:  Greek mathematicians had come up with solutions to the quadratic formula that used a straightedge and compass, but Khayyam conjectured that it was not possible to solve the cubic equation with just those tools, and so developed other means of finding the solutions geometrically, using a parabola.  (It would be more accurate to say solutions to cubic equations: although we write it as a single equation, at that time the quadratic and cubic equations were written as several different cases depending on whether the coefficients were positive or negative.)  It was 500 years before anyone found a more general solution than his.

Omar Khayyam was one of the earliest people to describe the Arithmetic triangle (which is sometimes called Pascal’s triangle, although this was 500 years before Blaise Pascal).  He also contributed to the fields of non-Euclidean geometry and number theory.

In addition to mathematics, Khayyam wrote about astronomy, geography, and music.  He is largely remembered for his poetry, especially the rubaiyat (aka  Rubā‘iyyāt, or quatrains)

The Moving Finger writes, and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.

(Translated into English by Edward Fitzgerald)

Khayamm passed away in Nishapur in 1131, and a mausoleum stands over his tomb


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