Presented from the viewpoint of the history of mathematics this book explores both
epistemological aspects of Chinese traditional mathematical astronomy and lunisolar calendrical
calculations. The following issues are addressed: (1) connections with non-Chinese cultural
areas (2) the possibility or impossibility of using mathematics to predict astronomical
phenomena a question that was constantly raised by the Chinese from antiquity through medieval
times (3) the modes of representation of numbers and in particular the zero found in the
context of Chinese calendrical calculations and (4) a detailed analysis of lunisolar
calendrical calculations. Fully worked-out examples and comparisons between the results of
calculations and the content of Chinese historical calendars from various periods are provided.
Traditional Chinese calendrical and mathematical astronomy consists of permanently reformed
mathematical procedures designed to predict but not explain phenomena pertaining to astronomy
and related areas. Yet despite appearances models of the mathematical techniques hidden
behind this voluminous corpus reveal that they depend on a limited number of clear-cut
mathematical structures. Although only a small fraction of these techniques have been fully
studied what is known surprisingly broadens our knowledge of the history of Chinese
mathematics. Sinologists interested in the history of Chinese science and anyone interested in
the history of Chinese mathematics the Chinese calendar and the history of Chinese
mathematical astronomy from its origin (104 BC) to its European reform (AD 1644) will find this
book very useful. The present English language edition is a fully revised and updated version
of the French original. Even though this is a research monograph in sinology no particular
sinological background is required although a basic understanding of 'concrete mathematics' is
needed. From the reviews of the French edition: This is a demanding rigorous book to read ...
worth the concentrated study it requires. The rewards are not only in the details but in the
general overview that ...[it] provides. Joseph Dauben EASTM 2011 ...first Work in a Western
language to turn to for anyone interested in the details of Chinese calendrical computations.
Benno Van Dalen ISIS 2011 Martzloff's careful scholarship and his overall look at the
calendar beyond astronomical calculations ... make this book a most valuable contributions to
a field of increasing interest. U. D'Ambrosio Mathematical Reviews 2013
