Leonhard Euler

Leonhard Euler
Author: Robert E. Bradley,Charles Edward Sandifer
Publsiher: Elsevier Science Limited
Total Pages: 534
Release: 2007
ISBN: 9780444527288
Category: Mathematics
Language: EN, FR, DE, ES & NL

Leonhard Euler Book Excerpt:

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich - New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova - New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Leonhard Euler

Leonhard Euler
Author: Robert E. Bradley,Ed Sandifer
Publsiher: Elsevier
Total Pages: 542
Release: 2007-03-20
ISBN: 9780080471297
Category: Mathematics
Language: EN, FR, DE, ES & NL

Leonhard Euler Book Excerpt:

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich - New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova - New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Leonhard Euler

Leonhard Euler
Author: Ronald S. Calinger
Publsiher: Princeton University Press
Total Pages: 689
Release: 2019-12-03
ISBN: 0691196400
Category: Biography & Autobiography
Language: EN, FR, DE, ES & NL

Leonhard Euler Book Excerpt:

"This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.

Leonhard Euler s Letters to a German Princess

Leonhard Euler s Letters to a German Princess
Author: Ronald S Calinger,Ekaterina (Katya) Denisova,Elena N Polyakhova
Publsiher: Morgan & Claypool Publishers
Total Pages: 215
Release: 2019-06-28
ISBN: 164327192X
Category: Science
Language: EN, FR, DE, ES & NL

Leonhard Euler s Letters to a German Princess Book Excerpt:

Leonhard Euler's Letters to a German Princess: A Milestone in the History of Physics Textbooks and More is a milestone in the history of physics textbooks and the instruction of women in the sciences. It also covers views of its author on epistemology, religion, and innovations in scientific equipment, including telescopes and microscopes. Today, 250 years later, we study this work of Euler's as a foundation for the history of physics teaching and analyze the letters from an historical and pedagogical point of view.

Leonhard Euler and the Foundations of Celestial Mechanics

Leonhard Euler and the Foundations of Celestial Mechanics
Author: Dora Musielak
Publsiher: Springer Nature
Total Pages: 228
Release: 2022-11-01
ISBN: 3031123220
Category: Science
Language: EN, FR, DE, ES & NL

Leonhard Euler and the Foundations of Celestial Mechanics Book Excerpt:

The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.

The Bloomsbury Companion to Kant

The Bloomsbury Companion to Kant
Author: Gary Banham,Dennis Schulting,Nigel Hems
Publsiher: Bloomsbury Publishing
Total Pages: 432
Release: 2015-01-29
ISBN: 1472586808
Category: Philosophy
Language: EN, FR, DE, ES & NL

The Bloomsbury Companion to Kant Book Excerpt:

Immanuel Kant is widely considered to be the most important and influential thinker of modern Europe and the late Enlightenment. His philosophy is extraordinarily wide-ranging and his influence has been pervasive throughout eighteenth, nineteenth and twentieth-century thought, in particular in the work of the German Idealists, and also in both Analytic and Continental philosophy today. Now available as a new and expanded edition in paperback, this accessible companion to Kant features more than 100 specially commissioned entries, written by a team of experts in the field, covering every aspect of his philosophy. The Bloomsbury Companion to Kant presents a comprehensive overview of the historical and philosophical context in which Kant wrote and the various features, themes and topics apparent in his thought. It also includes extensive synopses of all his major published works and a survey of the key lines of reception and influence including a new addition on Schopenhauer's reception of Kant. It concludes with a thorough bibliography of English language secondary literature, now expanded for this edition to include all cutting-edge publications in the area. This is an essential and practical research tool for those working in the field of eighteenth-century German philosophy and Kant.

The Legacy of Leonhard Euler

The Legacy of Leonhard Euler
Author: Lokenath Debnath
Publsiher: World Scientific
Total Pages: 420
Release: 2010
ISBN: 1848165269
Category: Mathematics
Language: EN, FR, DE, ES & NL

The Legacy of Leonhard Euler Book Excerpt:

This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler''s Contributions to Number Theory and Algebra; Euler''s Contributions to Geometry and Spherical Trigonometry; Euler''s Formula for Polyhedra, Topology and Graph Theory; Euler''s Contributions to Calculus and Analysis; Euler''s Contributions to the Infinite Series and the Zeta Function; Euler''s Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler''s Contributions to Mechanics and Elasticity; Euler''s Work on the Probability Theory; Euler''s Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.

Navigational Enterprises in Europe and its Empires 1730 1850

Navigational Enterprises in Europe and its Empires  1730   1850
Author: Rebekah Higgitt,Richard Dunn,Peter Jones
Publsiher: Springer
Total Pages: 259
Release: 2016-02-19
ISBN: 1137520647
Category: History
Language: EN, FR, DE, ES & NL

Navigational Enterprises in Europe and its Empires 1730 1850 Book Excerpt:

This book explores the development of navigation in the eighteenth and nineteenth centuries. It examines the role of men of science, seamen and practitioners across Europe, and the realities of navigational practice, showing that old and new methods were complementary not exclusive, their use dependent on many competing factors.

How Euler Did Even More

How Euler Did Even More
Author: C. Edward Sandifer
Publsiher: The Mathematical Association of America
Total Pages: 254
Release: 2014-11-19
ISBN: 0883855844
Category: Mathematics
Language: EN, FR, DE, ES & NL

How Euler Did Even More Book Excerpt:

Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

The Doctrine of Triangles

The Doctrine of Triangles
Author: Glen Van Brummelen
Publsiher: Princeton University Press
Total Pages: 390
Release: 2021-06-08
ISBN: 0691179417
Category: MATHEMATICS
Language: EN, FR, DE, ES & NL

The Doctrine of Triangles Book Excerpt:

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.

Excursions in the History of Mathematics

Excursions in the History of Mathematics
Author: Israel Kleiner
Publsiher: Springer Science & Business Media
Total Pages: 347
Release: 2012-02-02
ISBN: 0817682686
Category: Mathematics
Language: EN, FR, DE, ES & NL

Excursions in the History of Mathematics Book Excerpt:

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

The Continuum Companion to Kant

The Continuum Companion to Kant
Author: Gary Banham,Dennis Schulting,Nigel Hems
Publsiher: A&C Black
Total Pages: 410
Release: 2012-02-16
ISBN: 144111257X
Category: Philosophy
Language: EN, FR, DE, ES & NL

The Continuum Companion to Kant Book Excerpt:

Including over 500 specially commissioned entries from a team of leading international scholars, this is an essential reference to Kant's thought, writings and continuing influence.

Euler s Gem

Euler s Gem
Author: David S. Richeson
Publsiher: Princeton University Press
Total Pages: 336
Release: 2019-07-23
ISBN: 0691191999
Category: Mathematics
Language: EN, FR, DE, ES & NL

Euler s Gem Book Excerpt:

How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

Euler s Pioneering Equation

Euler s Pioneering Equation
Author: Robin Wilson
Publsiher: Unknown
Total Pages: 170
Release: 2019-07-17
ISBN: 0198794932
Category: Equations
Language: EN, FR, DE, ES & NL

Euler s Pioneering Equation Book Excerpt:

In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.

Emilie du Ch telet between Leibniz and Newton

Emilie du Ch  telet between Leibniz and Newton
Author: Ruth Hagengruber
Publsiher: Springer Science & Business Media
Total Pages: 256
Release: 2011-10-29
ISBN: 9789400720930
Category: Philosophy
Language: EN, FR, DE, ES & NL

Emilie du Ch telet between Leibniz and Newton Book Excerpt:

Emilie du Châtelet was one of the most influential woman philosophers of the Enlightenment. Her writings on natural philosophy, physics, and mechanics had a decisive impact on important scientific debates of the 18th century. Particularly, she took an innovative and outstanding position in the controversy between Newton and Leibniz, one of the fundamental scientific discourses of that time. The contributions in this volume focus on this "Leibnitian turn". They analyze the nature and motivation of Emilie du Châtelet's synthesis of Newtonian and Leibnitian philosophy. Apart from the Institutions Physiques they deal with Emilie du Châtelet's annotated translation of Isaac Newton's Principia. The chapters presented here collectively demonstrate that her work was an essential contribution to the mediation between empiricist and rationalist positions in the history of science.

A Cultural History of the Senses in the Age of Enlightenment

A Cultural History of the Senses in the Age of Enlightenment
Author: Anne C. Vila
Publsiher: Bloomsbury Publishing
Total Pages: 288
Release: 2014-10-23
ISBN: 1474233104
Category: History
Language: EN, FR, DE, ES & NL

A Cultural History of the Senses in the Age of Enlightenment Book Excerpt:

This volume examines the varied ways in which the senses were perceived afresh during the Enlightenment. In addition to introducing new philosophical and scientific models which sometimes upended the classic hierarchy of the senses, this period witnessed major changes in living and working habits, including urbanization, travel and exploration, the invention of new sonic and visual media, and the rise of comfort and pleasure as values that cut across a range of social classes. As this volume shows, those developments inspired a wealth of sensorially stimulating styles of design, art, music, poetry, foodstuffs, material goods and modes of worship and entertainment. The volume also demonstrates the period's countervailing concern with managing the senses, evident in fields like natural philosophy, medicine, education, religion, and public hygiene. Finally, it explores some of the Enlightenment's desensualizing tendencies, like the separation of sensuous body from discerning mind in certain arenas of science and manufacturing, and the late 18th-century shift away from a politics of publicity, or intense visual and aural scrutiny, toward the secret ballot. A Cultural History of the Senses in the Age of Enlightenment presents essays on the following topics: the social life of the senses; urban sensations; the senses in the marketplace; the senses in religion; the senses in philosophy and science; medicine and the senses; the senses in literature; art and the senses; and sensory media.

Ruggiero Boscovich s Theory of Natural Philosophy

Ruggiero Boscovich   s Theory of Natural Philosophy
Author: Luca Guzzardi
Publsiher: Springer Nature
Total Pages: 198
Release: 2020-08-31
ISBN: 3030520935
Category: Science
Language: EN, FR, DE, ES & NL

Ruggiero Boscovich s Theory of Natural Philosophy Book Excerpt:

Drawing on published works, correspondence and manuscripts, this book offers the most comprehensive reconstruction of Boscovich’s theory within its historical context. It explains the genesis and theoretical as well as epistemological underpinnings in light of the Jesuit tradition to which Boscovich belonged, and contrasts his ideas with those of Newton, Leibniz, and their legacy. Finally, it debates crucial issues in early-modern physical science such as the concept of force, the particle-like structure of matter, the idea of material points and the notion of continuity, and shares novel insights on Boscovich’s alleged influence on later developments in physics. With its attempt to reduce all natural forces to one single law, Boscovich’s Theory of Natural Philosophy, published in 1758, left a lasting impression on scientists and philosophers of every age regarding the fundamental unity of physical phenomena. The theory argues that every pair of material points is subject to one mutual force — and always the same force — which is their propensity to be mutually attracted or repelled, depending on their distance from one another. Furthermore, the action of this unique force is visualized through a famous diagram that fascinated generations of scientists. But his understanding of key terms of the theory — such as the notion of force involved and the very idea of a material point — is only ostensibly similar to our current conceptual framework. Indeed, it needs to be clarified within the plurality of contexts in which it has emerged rather than being considered in view of later developments. The book is recommended for scholars and students interested in the ideas of the early modern period, especially historians and philosophers of science, mathematicians and physicists with an interest in the history of the discipline, and experts on Jesuit science and philosophy.

A Historian Looks Back

A Historian Looks Back
Author: Judith V. Grabiner
Publsiher: MAA
Total Pages: 307
Release: 2010-10-14
ISBN: 0883855720
Category: Mathematics
Language: EN, FR, DE, ES & NL

A Historian Looks Back Book Excerpt:

Judith Grabiner, the author of A Historian Looks Back, has long been interested in investigating what mathematicians actually do, and how mathematics actually has developed. She addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. This book brings together much of what she has had to say to this audience. The centerpiece of the book is The Calculus as Algebra: J.-L. Lagrange, 1736-1813. The book describes the achievements, setbacks, and influence of Lagrange's pioneering attempt to reduce the calculus to algebra. Nine additional articles round out the book describing the history of the derivative; the origin of delta-epsilon proofs; Descartes and problem solving; the contrast between the calculus of Newton and Maclaurin, and that of Lagrange; Maclaurin's way of doing mathematics and science and his surprisingly important influence; some widely held “myths” about the history of mathematics; Lagrange's attempt to prove Euclid's parallel postulate; and the central role that mathematics has played throughout the history of western civilization. The development of mathematics cannot be programmed or predicted. Still, seeing how ideas have been formed over time and what the difficulties were can help teachers find new ways to explain mathematics. Appreciating its cultural background can humanize mathematics for students. And famous mathematicians' struggles and successes should interest -- and perhaps inspire -- researchers. Readers will see not only what the mathematical past was like, but also how important parts of the mathematical present came to be.

1001 Ideas that Changed the Way We Think

1001 Ideas that Changed the Way We Think
Author: Robert Arp
Publsiher: Hachette UK
Total Pages: 960
Release: 2018-03-12
ISBN: 178840050X
Category: Philosophy
Language: EN, FR, DE, ES & NL

1001 Ideas that Changed the Way We Think Book Excerpt:

An awe-inspiring overview of the development of human knowledge over the centuries! Part of the highly successful '1001' series which have sold over a million copies in the UK alone 1001 Ideas That Changed The Way We Think offers not only a comprehensive history of ideas, but also an eminently browsable source of amusement. This richly informative and entertaining book provides a wide variety of answers to those eternal questions such as... How was the universe created and what is the place of humans within it? How should a person live? And how can we build a just society? Readers will discover how the Greek philosopher Zeno 'proved' a flying arrow never moves and the mathematical proof of the existence of life in other galaxies. The inspiring ideas explored range from Gandhi's theory of civil disobedience to Mary Wollstonecraft's groundbreaking advocacy of women's rights. A wide variety of cultural movements are also covered, including Neoclassicism, Surrealism and Postmodernism. Drawing of a wide spectrum of topics including politics, cosmology, the arts, philosophy and religious beliefs, 1001 Ideas That Changed The Way We Thinktraces the exponential growth of human knowledge across the centuries. Ranging from the ancient wisdom of Confucius and Plato, to the cutting-edge theories taking shape in the twenty-first century, this book offers a wealth of stimulation and wit for any reader with a lively and curious mind.

Calendrical Calculations

Calendrical Calculations
Author: Edward M. Reingold,Nachum Dershowitz
Publsiher: Cambridge University Press
Total Pages: 135
Release: 2018-04-05
ISBN: 1108548032
Category: Computers
Language: EN, FR, DE, ES & NL

Calendrical Calculations Book Excerpt:

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.