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Leap Year – In Other Countries

Posted by jase on July 27, 2009

The Gregorian calendar, used by most western countries, recognizes an extra day at the end of February every four years except centenary years not divisible by 400. However, some cultures use calendars that do not apply the same leap year rules as the Gregorian calendar.

Some calendars, such as the Iranian calendar, do not observe February 29 as a leap day. Other calendars, such as the Chinese calendar, recognize a leap month. A few calendars that do not follow the conventional leap year model are listed below.  

Chinese Leap Year

The Chinese leap year has 13 months. A leap month is added to the Chinese calendar about every three years. The name of a leap month is the same as previous lunar month. The leap month’s place in the Chinese calendar varies from year to year. Unlike the Gregorian calendar, 2006 was a leap year in the Chinese calendar.

To determine a leap year, calculate the number of new moons between the 11th month in one year and the 11th month in the following year. A leap month is inserted if there are 13 moons from the start of the 11th month in the first year to the start of the 11th month in the next year. The leap month does not contain a principal term (Zhongqi). The Chinese calendar has been used for centuries and observes the movement of the sun, moon and stars. 

Jewish Leap Year

Like the Chinese calendar, the Jewish calendar has 13 months in a leap year. There are 29 or 30 days in each month in a Jewish leap year, which has 383, 384, or 385 days. An extra month, Adar I, is added after the month of Shevat and before the month of Adar in a leap year. According to Jewish tradition, Adar is a lucky and happy month.

A leap year is referred to in Hebrew as Shanah Me’uberet, or a pregnant year. A Jewish leap year occurs seven times in a 19-year cycle. The 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years are leap years in this cycle.  

Iranian Leap Year

There are about eight leap years in every 33-year cycle in the Iranian (or Persian) calendar. An extra day is added to the last month in a leap year. Leaps years occur when there are 366 days between two New Year’s days. However, it is not universally accepted that the calendar is solely based on observing the vernal equinox.

Leap years usually occur every four years. After every six or seven leap years, the Iranian calendar provides for a leap year that occurs on the fifth year instead of the fourth year. A period of 2820 years was the base for calculations to establish the frequency of a leap year occurring on the fifth year. At the start and the end of the 2820-year cycle, the vernal equinox takes place exactly at the same time of the tropical year.  

The Iranian calendar dates back to the 11th century, when a panel of scientists created a calendar that was more accurate than other calendars at the time. Although some changes have been made to the calendar, it is slightly more accurate than the Gregorian calendar. Compared with the Gregorian calendar, which errors by one day in about every 3226 years, the Iranian calendar needs a one-day correction in about every 141,000 years.  

Hindu Leap Year

The Hindu calendar inserts an extra month, often referred to as Adhika Maas, in a leap year. Adhika Maas typically occurs once every three years or four times in 11 years. Therefore the yearly lag of a lunar year is adjusted every three years. This adjustment allows for Hindu festivals tend to occur within a given span rather than on a set day.

The Indian National Calendar and the Revised Bangla Calendar of Bangladesh organize their leap years so their leap day is close to February 29 in the Gregorian calendar.  

Islamic Leap Year

In the Islamic Hijri calendar one extra day is added to the last month (making it 30 days instead of 29 days) in a leap year. This month, Dhu ‘l-Hidjdja, is also referred to as the month of the Hajj – the Muslim pilgrimage to Mecca. The Hijri calendar has a 30-year cycle with 11 leap years of 355 days and 19 years of 354 days. In the long term, it is accurate to about one day in 2500 years.

The leap year occurs in the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th and 29th years of the 30-year cycle. Leap months are forbidden by the Qur’an. The calendar is based on the Qur’an and its proper observance is a sacred duty for Muslims. It is a purely lunar calendar and contains 12 months that are based on the moon’s motion.  

Bahá’í Leap Year

The Bahá’í year begins on March 21 and is divided into 19 months of 19 days each, totaling 361 days. Four or five intercalary days are added to raise the number of days to 365, or 366 in leap years. The leap day is inserted in the days of Ayyam-i-ha , a period of intercalary days devoted to fasting preparations, hospitality, charity and gift-giving from February 26 to March 1.

Ethiopian Leap Year

The Ethiopian calendar is very similar to the Egyptian Coptic calendar, which has 13 months. Like the Coptic calendar, the Ethiopian calendar adds an extra day to the end of the year once every four years. The Ethiopian and Coptic calendars consist of 13 months, where the first 12 months each have 30 days and the 13th month has six days in a leap year instead of five days in a standard year.

Other Leap Years

Greece converted to the Gregorian calendar in 1924, although there is debate that the change may have occurred in 1920 or as early as 1916. There is discussion that some Orthodox Christians prefer to use a revised Julian calendar, where there is a discrepancy with the Gregorian calendar with regard to a leap year that will occur in 2800.

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Profile: Omar Khayyam

Posted by jase on July 5, 2009

Omar Khayyam (Persian: عمر خیام), (born 1048 AD, Neyshapur, Iran—1123 AD, Neyshapur, Iran), was a Persian polymath, mathematician, philosopher, astronomer and poet.

He has also become established as one of the major mathematicians and astronomers of the medieval period. Recognized as the author of the most important treatise on algebra before modern times as reflected in his Treatise on Demonstration of Problems of Algebra giving a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He also contributed to calendar reform and may have proposed a heliocentric theory well before Copernicus.

His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Zamakhshari referred to him as “the philosopher of the world”. Many sources have also testified that he taught for decades the philosophy of Ibn Sina in Nishapur where Khayyam lived most of his life, breathed his last, and was buried and where his mausoleum remains today a masterpiece of Iranian architecture visited by many people every year.

Outside Iran and Persian speaking countries, Khayyam has had impact on literature and societies through translation and works of scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde (1636–1703) was the first non-Persian to study him. However the most influential of all was Edward FitzGerald (1809–83)[4] who made Khayyam the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyam’s rather small number of quatrains (rubaiyaas) in Rubaiyat of Omar Khayyam.

Omar Khayyam was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe.

Like most Persian mathematicians of the period, Omar Khayyám was also famous as an astronomer.  Omar Khayyam was part of a panel that introduced several reforms to the Persian calendar, largely based on ideas from the Hindu calendar. On March 15, 1079, Sultan Malik Shah I accepted this corrected calendar as the official Persian calendar.  Omar Khayyám also built a star map (now lost), which was famous in the Persian and Islamic world.

It is said that Omar Khayyam also estimated and proved to an audience that included the then-prestigious and most respected scholar Imam Ghazali, that the universe is not moving around earth as was believed by all at that time. By constructing a revolving platform and simple arrangement of the star charts lit by candles around the circular walls of the room, he demonstrated that earth revolves on its axis, bringing into view different constellations throughout the night and day (completing a one-day cycle). He also elaborated that stars are stationary objects in space which, if moving around earth, would have been burnt to cinders due to their large mass. Some of these ideas may have been transmitted to Western science after the Renaissance.

Omar Khayyám’s poetic work has eclipsed his fame as a mathematician and scientist.

He is believed to have written about a thousand four-line verses or quatrains (rubaai’s). In the English-speaking world, he was introduced through the Rubáiyát of Omar Khayyám which are rather free-wheeling English translations by Edward FitzGerald (1809-1883).

Other translations of parts of the rubáiyát (rubáiyát meaning “quatrains”) exist, but FitzGerald’s are the most well known. Translations also exist in languages other than English.

Ironically, FitzGerald’s translations reintroduced Khayyam to Iranians “who had long ignored the Neishapouri poet.” A 1934 book by one of Iran’s most prominent writers, Sadeq Hedayat, Songs of Khayyam, (Taranehha-ye Khayyam) is said have “shaped the way a generation of Iranians viewed” the poet.

Omar Khayyam’s personal beliefs are not known with certainty, but much is discernible from his poetic oeuvre.

Despite strong Islamic training, it is clear that Omar Khayyam himself was undevout and had no sympathy with popular religion, but the verse: “Enjoy wine and women and don’t be afraid, God has compassion,” suggests that he wasn’t an atheist. Some religious Iranians have argued that Khayyam’s references to intoxication in the Rubaiyat were actually the intoxication of the religious worshiper with his Divine Beloved – a Sufi conceit. This however, is reportedly a minority opinion dismissed as wishful pious thinking by most Iranians.

It is almost certain that Khayyám objected to the notion that every particular event and phenomenon was the result of divine intervention. Nor did he believe in an afterlife with a Judgment Day or rewards and punishments. Instead, he supported the view that laws of nature explained all phenomena of observed life. One hostile orthodox account of him shows him as “versed in all the wisdom of the Greeks” and as insistent that studying science on Greek lines is necessary. He came into conflict with religious officials several times, and had to explain his views on Islam on multiple occasions; there is even one story about a treacherous pupil who tried to bring him into public odium. The contemporary Ibn al Kifti wrote that Omar Khayyam “performed pilgrimages not from piety but from fear” of his contemporaries who divined his unbelief.

Khayyám’s disdain of Islam in general and its various aspects such as eschatology, Islamic taboos and divine revelation are clearly visible in his writings, particularly the quatrains, which as a rule reflect his intrinsic conclusions describing those who claim to receive God’s word as maggot-minded fanatics.

Khayyam himself rejects to be associated with the title falsafi- (lit. philosopher) in the sense of Aristotelian one and stressed he wishes “to know who I am”. In the context of philosophers he was labeled by some of his contemporaries as “detached from divine blessings”.

Khayyam the philosopher could be understood from two rather distinct sources. One is through his Rubaiyat and the other through his own works in light of the intellectual and social conditions of his time.  The latter could be informed by the evaluations of Khayyam’s works by scholars and philosophers such as Bayhaqi, Nezami Aruzi, and Zamakhshari and also Sufi poets and writers Attar Nishapuri and Najmeddin Razi.

As a mathematician, Khayam has made fundamental contributions to the Philosophy of mathematics especially in the context of Persian Mathematics and Persian philosophy with which most of the other Persian scientists and philosophers such as Avicenna, Biruni, and Tusi are associated. There are at least three basic mathematical ideas of strong philosophical dimensions that can be associated with Khayyam.

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