Bresenham's algorithm minimizes error in drawing lines on integer grid
points; leap year calculations, surprisingly, are a generalization. We
compare the two calculations, and show how to compute directly, without
iteration, individual points of a Bresenham line. We also discuss an
unexpected connection of the leap year/line pattern with Euclid's algorithm
for computing the greatest common divisor.
(PDF; 13 pages)
By Nachum Dershowitz and Edward M. Reingold.
The 24th IAJGS International Conference on Jewish Genealogy,
Jerusalem, July 4-9, 2004.
Ancient Indian Leaps in the Advent of Mathematics
edited by B. S. Yadav (2005).
We analyze various Indian calendars. We discuss the Indian day count, a
generic solar calendar that generalizes various calendars including the mean
Indian solar calendar, the true and astronomical Indian solar calendars, a
generic lunisolar calendar that generalizes the Indian version, and the true
and astronomical Indian lunisolar calendars. We also discuss aspects of the
traditional Indian calculation of the time of sunrise and the determination of
(PDF; 25 pages)
Birashkname (Musa Akrami, editor),
University of Shahid Beheshti, 1998.
In this note we describe a unified implementation of calendars whose year
is based on the astronomical solar cycle--that is, on the precise solar
longitude at a specified time. For example, the astronomical Persian calendar
begins its new year on the day when the vernal equinox (approximately March
21) occurs before apparent noon (the middle point of the day, not clock time)
and is postponed to the next day if the equinox is after apparent noon. Other
calendars of this type include the French Revolutionary calendar and the
future form of the Bahai calendar. Our approach also offers a slight
simplification to the implementation of the Chinese lunisolar calendar.
(PostScript; 7 pages)
Software-Practice and Experience20 (1990), 899-928.
A unified, algorithmic presentation is given for the Gregorian (current
civil), ISO, Julian (old civil), Islamic (Moslem), and Hebrew (Jewish)
calendars. Easy conversion among these calendars is a byproduct of the
approach, as is the determination of secular and religious holidays.
(PostScript; 30 pages)