Showing posts with label Omar Khayyam. Show all posts
Showing posts with label Omar Khayyam. Show all posts

Friday, December 6, 2013

The Jalāli Calendar

Syrian Astrolabe
Yesterday I mentioned that Omar Khayyam spent some of his time working on calendar reform. This was not the same calendar reform being done in the Christian world, however. The Persian calendar was—and still is—far more accurate than the Gregorian calendar.

Originally, the Persian calendar was lunar, following the 28-day cycle of the Moon. Since the year does not fit into an equal number of lunar cycles, however, the lunar calendar creates "seasonal drift" without a lot of alterations. This calendar was begun over 1000 years BCE. Khayyam was one of several scholars using astronomical observations to create a revised version. It was approved on 15 March 1079 by the Seljuk Sultan, Malik Shah I.

Khayyam and his team calculated the length of the year to be 365.24219858156 days; modern science puts it at 365.2422464 days. Some aspects of the new calendar:

  • The year started within a day of March 21st, the vernal equinox
  • Months were based on when the sun transited to a new sign of the zodiac, not 12:00AM
  • Months could last from 29-32 days, and
  • Months could change their length from year to year

That 4th point is because of the 2nd point. Months weren't given arbitrary numbers of days as in the West. The Jalāli calendar depended on strict astronomical data, not cultural numerical choices. Therefore, the 6th month of the year might have 30 days one year and 31 days the next, depending on when the sun passed across the line in the sky that separated the zodiacal signs. It also means that seasonal drift—the tendency of seasons to start and end on widely varying dates over time—never exceeded one day. Leap years were unnecessary.

Eventually, the varying length of the months was considered a liability. The calendar—still used in Iran and Afghanistan—was changed in 1925 in order to have a more regular look and to save the hassle of applying the results of constant astronomical observation.

Thursday, December 5, 2013

Omar Khayyam, Mathematician

First page of "Cubic equation and
intersection of conic sections"
A book of verses underneath the bough
A flask of wine, a loaf of bread and thou
Beside me singing in the wilderness
And wilderness is paradise now.

The Rubaiyat of Omar Khayyam, translated by Edward Fitzgerald in 1859, made Khayyam the most famous Persian poet in the 19th century. Few people realize that Khayyam did not need Fitzgerald to be famous. Centuries earlier, he was one of the most influential thinkers produced by the Middle East.

Born in Nishapur on the 18th of May in 1048, he spent part of his youth in Balkh, which would produce Rumi 80 years after Khayyam's death. He studied under the well-known scholars Mansuri and Nishapuri. He put his education to work: as an adult, he was either teaching algebra and geometry, studying the stars, working on calendar reform, acting as a court advisor, or learning medicine. He taught the works of Avicenna.
The Tomb

He was best known in his lifetime and afterward for his mathematical writing, especially on algebra. Many of the principles of algebra that made their way to Europe came from Khayyam's Treatise on Demonstration of Problems on Algebra (1070).

One of his claims was that the solution of cubic equations cannot be solved by a ruler and compass. He said it required the use of conic sections, and announced his intention to write a paper that lays out the "fourteen forms with all their branches and cases." He never got around to it, and 750 years would have to pass before someone produced the proof of Khayyam's claim.

Omar Khayyam died on 4 December 1131 at the age of 83, and was buried in what is now the Khayyam Garden in Nishapur. A  mausoleum was built in 1963 to house his remains.