This book makes accurate calendrical algorithms readily available for computer use.

An invaluable resource for working programmers, as well as a fount of useful algorithmic tools for computer scientists, astronomers, and other calendar enthusiasts, The Ultimate Edition updates and expands the previous edition to achieve more accurate results and present new calendar variants. The book now includes coverage of Unix dates, Italian time, the Akan, Icelandic, Saudi Arabian Umm al-Qura, and Babylonian calendars. There are also expanded treatments of the observational Islamic and Hebrew calendars and brief discussions of the Samaritan and Nepalese calendars. Several of the astronomical functions have been rewritten to produce more accurate results and to include calculations of moonrise and moonset. The authors frame the calendars of the world in a completely algorithmic form, allowing easy conversion among these calendars and the determination of secular and religious holidays. LISP code for all the algorithms is available in machine-readable form.

Expanded coverage includes generic cyclical calendars, astronomical lunar calendars, and the Korean, Vietnamese, Aztec, and Tibetan calendars.

An invaluable resource for working programmers, as well as a fount of useful algorithmic tools for computer scientists, astronomers, and other calendar enthusiasts, The Ultimate Edition updates and expands the previous edition to achieve more accurate results and present new calendar variants. The book now includes coverage of Unix dates, Italian time, the Akan, Icelandic, Saudi Arabian Umm al-Qura, and Babylonian calendars. There are also expanded treatments of the observational Islamic and Hebrew calendars and brief discussions of the Samaritan and Nepalese calendars. Several of the astronomical functions have been rewritten to produce more accurate results and to include calculations of moonrise and moonset. The authors frame the calendars of the world in a completely algorithmic form, allowing easy conversion among these calendars and the determination of secular and religious holidays. LISP code for all the algorithms is available in machine-readable form.

Simultaneously displays the date on thirteen different calendars over a three-hundred year period.

The Calendar was invented in ancient times to allow nations to pace their economic and social activities with climatic seasons. Throughout the history of civilizations, much depended on organizing and administering an accurate calendar. Hunter-gatherers needed the calendar to predict the migrations of herds of wild animals. As humanity advanced, farming communities required calendars to predict the coming of rain or the time of the flooding of rivers. Traders and seafaring communities needed to map the best time of the year to tackle the dangers of seas when sailing far from home. In contemporary times of globalization, calendars have become even more critical in optimizing the complex supply chains of local and global production cycles. Oral traditions ascertain that the Arabs of the Arabian Peninsula used a rudimentary lunisolar calendar, called in the literature the “Arabian Calendar.” Like with all nations, the lunisolar Arabian Calendar helped the Arabs organize their meager resources in the best ways possible. For example, research showed that the Ḥajj season and its pan-Arabian markets were scheduled to coincide with the date harvesting season peaking from July to September. The abundance of the date harvest available in this period, along with assigning the concept of inviolability to the Arabian months spanning this season, allowed them to travel across Arabia to Mecca to trade in the pan-Arabian markets and to participate in the religious rituals of their pilgrimage (the Ḥajj). It is asserted in this book that Prophet Muḥammad followed the lunisolar Arabian Calendar all his life. At the end of the tenth year after he migrated from Mecca to Medīna, and during his Farewell Pilgrimage, the Qurʾān sternly abolished the process of intercalation, i.e., the Nasīʾ, the very process which allowed the Arabs to organize their various economic and religious activities. When Caliph ʿUmar ibn al-Khaṭṭāb initiated the Hijri Calendar seven years after Prophet Muḥammad death, i.e., in 17 AH, he founded it as “purely lunar,” which meant its months were allowed to float within the solar year. Caliph ʿUmar is famous for his zeal in protecting the fundamental Islamic principle of monotheism. This, I show, was the reason for introducing the Hijri Calendar as purely lunar, because “Nasīʾ,” i.e., Quraysh’s method of intercalation was hopelessly entangled with the polytheistic religion of Quraysh, the Prophet’s tribe, and the guardian of the holy places in Mecca and its environs. The harmful effects of following the purely lunar Hijri Calendar were realized from early on. But the prohibition of Nasīʾ inhibited the early Islamic caliphs from reforming the Hijri Calendar. This book explores the history of the Arabian Calendar and its intimate connection with the Hijri Calendar. The main findings of this book are as follows: 1- The main Ḥajj shrines in Macca are aligned in the direction of sunrises and sunsets of the Summer Solstice day. 2- Quraysh intercalated its Arabian Calendar by forcing the Summer Solstice (SS) Day to occur within the 11th month of the Arabian Calendar, Shawwāl. The Nasīʾ month was added when the onset of the SS was about to transfer to into the 11th month Dhū’l Qaʿda. 3- The onset of the SS day was determined through the sunset alignment along the line joining the posts of “al-Wosṭā and al-ʿAqaba Jamarāt, and also by observing the sun rising from behind the peak of mount Thabīr from the location of the sacrificial altar of pre-Islamic Mina. 4- The Prophet arrived in his migration from Mecca to Medīna on the Days of ʿĀshūrāʾ which corresponded to the dates of 8th of Rabīʿ-I, the 10th of the Hebrew month Tishri, and to the 23rd of September 632. 5- The epoch of the Hijri Calendar must be adjusted back by two days from the epoch used so far. 6- The Farewell Pilgrimage occurred in autumn on September 4, 632 CE, not in spring on March 11, 632 CE.

In On Their Own Terms, Benjamin A. Elman offers a much-needed synthesis of early Chinese science during the Jesuit period (1600-1800) and the modern sciences as they evolved in China under Protestant influence (1840s-1900). By 1600 Europe was ahead of Asia in producing basic machines, such as clocks, levers, and pulleys, that would be necessary for the mechanization of agriculture and industry. In the seventeenth and eighteenth centuries, Elman shows, Europeans still sought from the Chinese their secrets of producing silk, fine textiles, and porcelain, as well as large-scale tea cultivation. Chinese literati borrowed in turn new algebraic notations of Hindu-Arabic origin, Tychonic cosmology, Euclidian geometry, and various computational advances. Since the middle of the nineteenth century, imperial reformers, early Republicans, Guomindang party cadres, and Chinese Communists have all prioritized science and technology. In this book, Elman gives a nuanced account of the ways in which native Chinese science evolved over four centuries, under the influence of both Jesuit and Protestant missionaries. In the end, he argues, the Chinese produced modern science on their own terms.