History of Mathematics Bibliography

Collected and annotated by students in the History of Mathematics class
Department of Mathematics Education
University of Georgia
1996-1997

A

Aaboe, A. (1964). Episodes from the early history of mathematics. New York: Random House Publishers.
(1) The information in this book is limited to four historical areas: Babylonian Mathematics, Early Greek mathematics with Euclid's construction of the regular pentagon, Archimedean mathematics (three samples) and Ptolemy's construction of a trigonometric table. The limited subject area provides an in-depth examination of selected problems and developments. Sample problems with solutions are provided. Also, there are nice illustrations and chapter summaries. (2).This book is one of a series written in order to make some important mathematical ideas interesting and understanding to a large audience of high school students and layman. Topics vary in difficulty. (3) This volume of the series includes four episodes from the early history of mathematics capable of independent treatment yet all having a common theme. High School/College, Babylonian and Greek. Science (3rd) QA22.A13.

Achelis, E. (1937). The world calendar reform since 1930. New York: G. P. Putnam's sons.
This book discusses the history of many different calendar types. It explains the options and reform of the calendar in 1930. It gives a clear and logical account of the progress of the calendar. The book has very interesting thoughts on the calendar's reform. It covers the appeal to women, League of Nations, religious considerations, and many other aspects. This book could be enjoyed by middle schools, high schools, and on the college level. Main (4th) CE73.A177.

Achelis, E. (1959). The calendar for the modern age. New York: Thomas Nelson Sons.
The book covers from the earliest moon, star and Egyptian calendar to the present Gregorian calendar. The author gives a clear picture of the movement throughout time. Chapters could be read separately and still be easily understood. The book discusses the religious importance of some specific dates. this book is very practical and could be used by many to help understand the calendar. Main (4th) CE73.A177c.

Anglin, W. S. , J. Lambek. (1995). The heritage of thales. A detailed look at the history of Thales. Science (3rd) QA21.A535.

Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. Pacific Grove, CA: Brooks/Cole Publishing Co.

B

Baker, C. (1996). How big was the Roman Empire? Mathematics Teaching in the Middle School. Vol. 1, 9, pp. 754-759.
The activity in this article was designed as part of a sixth-grade interdisciplinary unit, "seeing the World through the Eyes of Ancient Greeks and Romans." Aderhold (2nd) Curriculum Materials Center.

Ball, W. W. R. (1939). Mathematical recreations & essays. New York: Macmillan.
This book contains fourteen chapters detailing recreational mathematics in many different areas such as geometry and topology. The history of each problem is discussed and mathematical solutions are presented Mathematical "toys" are discussed along with their histories and ancient origins. High School/College, All Cultures. Science (3rd) QA95.B187.

Barnes, S. (1996). Perimeters, patterns, and pi. Mathematics Teacher. Vol. 89, 4. pp. 284-288.
It deals with some of the most common questions with Pi: How did those mathematicians of antiquity know to know 3. 14 for a ratio? and What did they do to find Pi? Main (2nd) LB1645.M4.


Bell, E. T. (1945). The development of mathematics. New York, NY: McGraw-Hill Book Company.
This is a broad account of the general development of mathematics with particular references to main concepts and methods. This is more a narrative in the development of mathematics with some reference to social implications. The reading is rather interesting, but there is very little problem solving. Science (3rd) QA21.B433.

Bell, E. T. (1961). Men of mathematics. New York: Simon and Schuster.
This books presents portraits of famous mathematicians. Although a brief discussion of Zeno, Eudoxus, and Archimedes is included, the book is mainly devoted to discussions of mathematicians from the 1500's to modern times. Even though famous problems are included in this book, the discussions of these famous men's lives are very fascinating, with many anecdotes included, making this book very interesting reading. High School/ College, All Cultures. Science (3rd) QA21.B42.

Bell, R. C. (1979). Board and table games from many civilizations.
This book is a two volume set bound as one. The games have been divided into six types depending upon their basic premise. The history of each game is discussed along with strategies for winning. Photographs of the games are included making for a nice visual in reading. Middle/High School/ College, All Cultures. Athens Regional Library 794 Bell (An older version, 1917 is available in Main (2nd) GV1312.B435b, published by New York: Oxford University Press).

Bennet, D. (1993). Exploring geometry with the Geometer's Sketchpad . Berkeley, California: Key Curriculum Press.
Chapter two entitled, "Transformations, Symmetry and Tesselations", contains discovery activities to be used with Geometer's Sketchpad. The directions are excellent and capable students can follow them independently.

Berggren, J. L. (1986). Episodes in the mathematics of medieval Islam. New York, NY: Springer-Verlag.
This book contains six chapters each with exercises and bibliography. The chapters cover the topics of Islamic arithmetic, geometrical constructions in the Islamic world, algebra in Islam as well as trigonometry and spherics in the Islamic world. This presentation is comprehensive and accessible to anyone with a background in high school mathematics. Science (3rd) QA27.A67B46.

Bolt, B. (1982). Mathematical activities: a research book for teachers. Cambridge: Cambridge University Press.
A collection of one hundred fifty-four games, puzzles, investigations, and projects that cover a wide variety of topics is available here as a resource for teachers. The activities are designed to stimulate and encourage students to develop appreciation of numbers, spatial concepts, and mathematical thinking. Science (3rd) QA16.B64.

Borst, A. (1993). The ordering of time: From the ancient computus to the modern computer. Great Britain: The University of Chicago Press.
The book shows accounts of measuring time. It spans throughout time and discusses calculable and allotted time. The book goes into great detail making it hard to understand and follow at times. It could have lost something in the translation from German to English. I would recommend it for college level only. Main(4th) CE6.B6713.

Bourbaki, N. (1984). Elements of the history of mathematics. Berlin: Springer-Verlag.
Not only does this book have elements of history of math, it allows us to see math from a different culture. Since it is translated from French we can compare math in France and USA. Science (3rd) QA21.B7613.

Boyer, C. B.(1968). A history of mathematics. New York, NY: John Wiley & Sons, Inc.
The topics explained in this text include the primitive origins of mathematics, many cultural histories of mathematics, several important mathematicians (examples: Euclid, Apollonius, Fermat, and Descartes), and mathematics in relation to different periods of time (Renaissance, Middle Ages, etc. ). The text is geared more toward college students than to high school. It shares many characteristics with Eves' book. Science (3rd) QA21.B767.

Brendan, B. T. (1965). How Ptolemy constructed trigonometry tables. Arithmetic Teacher. 58, 141-49. Main (2nd) LB1589.A7.

Brody, J. (1974). In advance of the ready-made. Kiva Murals and Navajo dry painting. In M. E. King & I. R. Traylor, Jr. Art and environment in Native America. Texas Text University Press. p. 11-22. Main (4th) E59.A7A68.

Bruck, R. H. (1971). A survey of binary systems. Berlin: Springer-Verlag.
This book is very complex and not very interesting to read. The emphasis is on theorems and proofs, but more highly developed parts of the subject have been discussed in detail. The use of certain symbols could make reading hard for some while easier for those who understand the terminology. The author places the symbols and their meanings in paragraph form making it harder to locate and understand. It would be easier for a novice to understand if the symbols and meanings were placed in a graph that could be flipped back when needed. Science (3rd) QA266.B7.

Buhler, W. K. (1981). Gauss, a biographical study. Berlin: Springer-Verlag.
This interesting biography describes the life of the mathematician and scientist Carl Friedrich Gauss. He lived in a period of extraordinary political and social development, but was able to accomplish a great deal in the scientific area. The author deals with family, social, and political effects on Gauss' development and his mathematics. Science (3rd) QA29.G3B83.

C

Cairns, T. (1986). The coming of civilization. Cambridge: Cambridge University Press. Information on ancient Greek civilization. Main (4th) D65. C35.

Cajori, F. (1928). A history of mathematical notations. Chicago: Open court publishing Company. Science (3rd) QA21.C139hi.

Calinger, R. (1995). Classics of mathematics. Englewood Cliffs, NJ: Prentice-Hall.
We see a broad coverage of mathematics in early civilizations. There are also highlights of the ancient Mediterranean and modern Europe, medieval Islam and India, as well as traditional China and the US. The chapters are divided with topical subdivisions and there are specific problems and focus on mathematicians. (An older version (1982). published by Oak Park, Ill.: Moore Pub. Co, is available in Science (3rd) QA21.C55).

Campbell, D. , & Higgins, J. (1984). Mathematics: people problems. Results Volume I. Belmont, CA: Wadsworth International.
The book includes three parts: historical sketches, some mathematical lives, and the development of mathematics. It is an "introduction to the spirit of mathematics. " The topics discussed include history on Japanese, Muslim, Greek, Egyptian, and Chinese mathematics as well as some women mathematicians. As a whole, it has many practical aspects.

Campbell, D., & Higgins, J. (1984). Mathematics: People Problems. Results Volume II. Belmont, CA: Wadsworth International.
A collection of articles, divided into three parts, this book deals with mathematical foundations as well as some development. It includes an excerpt from C. Henry Edwards, Jr. which was very interesting. Subjects discussed in the book include pi, e, non Euclidean geometry, group theory, and the invisible culture of mathematics. It is has both practical and theoretical aspects.

Campbell, D. , & Higgins, J. (1984). Mathematics: People, Problems, Results Volume III. Belmont, CA: Wadsworth International.
This book focuses on many aspects of mathematics in present times. However, it deals with the role of mathematics in industry during the first 75 years of industry in America. Other historical notes include references to famous non-mathematicians of the past and their dealings with mathematics. Also, mathematics in art and nature are discussed. It is both practical and theoretical.

Casas-Alvero, E. , Xambo-Descamps, S. (1986). The theory of conics. The enumerative theory of conics after Halphen. Science (3rd) QA3.L47.

Conway, J. H. (1996). The book of numbers. New York: Copernicus. Springer-Verlag.
This explanation of the ways in which the word "number" is used includes the development of numbers, a study of integers, and a section on special numbers. It is written for those without a particular mathematics background but with enough depth for teachers to learn new information in several areas. Color graphics enhance the section on "Doing Arithmetic and Algebra by Geometry. " History of mathematics is evident not only in the "development" section, but throughout the book. Science (3rd) QA241.C6897.

Coolidge, J. L. (1945). A history of the conic sections and quadric surfaces. Oxford, England: Clarendon Press. Discusses the evolution of the development of conic sections over the years. Science 3rd, QA559.C774h.

Coxford, A. (1993). Geometry: The University of Chicago School Mathematics Project. Glenview, Illinois: Scott, Foresman and Company.
The inclusion of historical vignettes and famous problems into the text and teaching suggestions makes this book of particular interest. It integrates algebra with the geometry, emphasizes reading and problem solving, uses real life situations, emphasizes the SPUR (skills, properties, uses, representations) approach, and combines a gradual practice and mastery learning approach.

Crowe, D. (1986). Symmetry. Rigid motions. and patterns. Arlington, VA: COMAP.
This book contains five sections of descriptions, definitions and applications of the four rigid motions in a plane. Motivated high school students can follow the discussion and complete the activities as independent study. This is an excellent source of enrichment material.

D

Daffa, A. & Stroyls, J. (1984). Studies in the exact sciences in medieval Islam. Dhahran, Saudi Arabia: University of Petroleu.
Focuses on Arabic transmission of Greek math. Also discusses numerical analysis from 9th to 15th century and geometric theory of equations. Plus an interesting discussion of attempt to prove parallel postulate. Science 3rd Q127.A5D31.

Darden, N. J. (1935). Standard reference calendar. Never out of date. Washington, DC: Standard Calendar Association.
This book gives instructions for the use of the Standard Reference Calendar. It includes a list of Anniversaries and holidays generally observed in the United States. The book suggests that this particular calendar has been designed to meet the requirements of business and professional people, but is also useful for students, or anyone who wishes to know accurately any date, past, present, or future, within the realm of modern chronology. One thing I found particularly interesting was the brief overview of the history of calendars. Main (4th) CE73.D216.

Dauben, J. W. (1985). The history of mathematics from antiquity to the present. New York, NY: Garland. Discusses the history of mathematics from ancient to modern times. Similar to what the textbook discusses. Science 3rd, QA21.D350.

David, F. N. (1962). Games, gods and gambling the origins and history of probability and statistical ideas from the earliest times. New York: Hafner publishing Co.
This book covers the history of probability and statistics. The author goes back to original documents to check mathematical developments. She discusses in great detail the contributors to probability such as Fermat, Pascal, Galileo and many others. The book contains the letters between Fermat and Pascal. This is very interesting to look at with great respect to Pascal's Triangle. Science (3rd) QA273.D249g.

DeLacy, E. A. (1963).Euclidean geometry and Euclid's biography. Euclid and Geometry. Aderhold (2nd) QA22.D332E.

Dieudonne, J. A. (1985). History of algebraic geometry: An outline of the history and development of algebraic geometry. Science(3rd) QA564.D513.

Dilke, O. A. W. (1987). Mathematics and measurement. University of California Press.
Greek mathematicians laid down the foundations of algebra and trigonometry. Trigonometry is thought to have begun with a work, now lost, by Hipparchus of Hicaea and Rhodes (c. 190- after 126 BC) on the chords of a circle. Ptolemy of Alexandria (who flourished in AD 127-48). built upon this and other investigations of Hipparchus in his work entitled Syntaxis.

Dilke, O. A. W. (1975). The ancient Romans: how they lived and worked. Newton Abbot: David & Charles.Main (4th) DG78.D55.

Domoryad, A. P. (1964). Mathematical games and pastimes.
This book is mainly devoted to a discussion of classical games, their origin, and their solutions. The mathematical knowledge required to enjoy this book ranges from 5th grade to high school. References are also given to books in which more detailed discussions of the topics may be found. Middle/High School/ College, All Cultures. Science (3rd) QA95.D643.

Dorrie, H. (1965). 100 great problems of elementary mathematics: their history and solution. New York: Dover Publications.
The author presents a collection of problems, explains their origin, and presents brief and understandable solutions. Most problems require only a basic knowledge of mathematics, however some do involve an understanding of analysis. Even though the origin of each problem is stated, this book has more details about its solution than the historical aspects of the problem. High School/College, All Cultures. Science (3rd) QA43.D613.

Doyle, T. M. (1996). The Civil War and the Standards: some mathematical activities. Mathematics Teaching in the Middle School. 1 (9). pp. 748-752.
This article introduces some activities that can illustrate to students the importance of using numerical-analysis skills to study history, as well as the importance of using mathematics to communicate and understand concepts. Aderhold (2nd) Curriculum Materials Center.

Dilke, O. A. (1987). Mathematics and measurement. Berkley, CA: University of California Press.
This work shows the separate development of mathematics and measurement by various civilizations. In addition, the author defines the influence or non-influence (in certain cases) of development by other civilizations. The subjects range from measurement, surveying and architecture, mapping to scale, telling time, trade and commerce, and leisure pursuits. Also, this book contains excellent illustrations. Science (3rd) QA22.D55.

Dunham, R. (1994). The mathematical universe: An alphabetic journey through the great proofs, problems, and personalities. New York, NY: John Wiley & Sons, Inc.
This is an A to Z look at math from a = arithmetic to z = complex numbers. In between are easy to read examples, histories and explanations of various concepts. The illustrations are good as well. (2). The book surveys the discipline of mathematics in an alphabetical format through a series of essays running from A to Z. The content includes a chapter on differential equations. Important historical notes of each are included. The mathematics is geared toward students who have completed high school algebra and geometry. The theme of the book is that mathematics is an ancient yet vital subject. High School/ College, All Cultures. Science (3rd) QA21.D785.

E

Eddins, S. (1994). Geometric Transformations-Part 1. Mathematics Teacher. 87(3)., 177-180.
This is an activity for grade levels 5-12. The objectives in the author's words are "create and describe geometric transformations, demonstrate the ability to give directions that will transform one triangle into its image triangle; be able to form and test conjectures and create extensions for problems introduced in class." Main (2nd) LB1645.M4.

Egan, P. (1979). History of Art. Englewood Cliffs, NJ: Prentice-Hall.
This survey of the major visual arts from the dawn of history to the present day includes a chapter on Islamic art and architecture. Many of the designs are tesselations.

Euclid. (1926). The thirteen books of Euclid's Elements. Translated by T. L. Heath. Cambridge: The University Press.

Eves, H. (1976). An introduction to the history of mathematics. New York. Holt, Rinehart and Winston.
This text gives an introduction to the history of mathematics. It covers all topics from arithmetic to calculus. It explains how, why, and when different topics arose and who developed these topics. It gives a complete history of mathematics from the ancient to the modern. High School/ College, All cultures, All times. Galin, Science (3rd) QA21.E8.

Eves, H. (1983). Great moments in mathematics. Before 1650. Washington, DC: The Mathematical Association of America.
This book is divided into twenty-three lectures and each contains historical background. Second, there is a nice presentation of problems and how they were developed and solved--hints are located in the back of the book. Fortunately, there are nice samples and illustrations. Science (3rd) QA21.E796.

Feinberg, C. (1996). The case of trapezoidal numbers. Mathematics Teacher. 89 (1). pp. 16-21.
This article shows that triangular numbers are a subset of trapezoidal numbers. It is an extension of the study of figurative numbers such as triangular numbers, square numbers, cubic numbers, and rectangular numbers. Main (2nd) LB1645.M4.

Field, J. V. & Gray, J. J. (1987). The geometrical work of Girard Desargues. New York, NY: Springer Verlag.
A biography and study of the work of the famous French mathematician, especially on his work with conic sections. Conic Sections. Science 3rd, QA485.D47.
Freebury, H. A. (1961). A history of mathematics. New York, NY: Macmillan.
Discusses the history and the development of mathematics and contributions by different cultures. History of mathematics. Science 3rd, QA21.F853h.

Fry, E. K & Glidden, P. L. (1996). Illustrating mathematical connections:
A geometric proof of Euler's Theorem. Mathematics Teacher. (89). (1). pp. 62-65. Emphasizes mathematical connections, promotes mathematical reasoning, and helps students become better problem-solvers. Main (2nd) LB1645.M4.

G

Garbarino, M. (1980). The Indian book. Chicago. World Book. Childcraft Annual.

Gardner, M. (1988). Time travel and other Mathematical bewilderments. New York: W. H. Freeman and Company.
The twelfth collection of the author's articles from Scientific American has some strange topics such as time travel, anamorphic art, the rubber rope problem, and curious maps of the world. But also included is a chapter entitled "Hexes and Stars" on figurative numbers and two excellent chapters on tessellation: "Tiling with Convex Polygons" and "Tiling with Polyominoes, Polyiamonds, and Polyhexes." Science (3rd) QA95.G325.

Gardner, M. (1959). The Scientific American book of mathematical puzzles and diversions.
This book is an earlier version of a compilation of columns written by the author for the magazine. These problems seem to be more elementary and could be enjoyed my students in lower grade levels. The author has a delightful sense of humor and the book makes very interesting reading. Middle/High School/ College, All Cultures. Science (3rd) QA95.G3.

Gardner, M. (1966). Martin Gardner's new mathematical diversions from Scientific American.
This book of mathematical "jokes" (mathematics mixed with a strong element of fun) is a compilation of columns written by the author for the magazine. Many interesting mathematical games and puzzles are described, their history discussed, and possible solutions are put forth. High School College, All Cultures. Science (3rd) QA95. G295.

Gerdes, P. (1994). Sona Geometry. Vol. 1. Maputo, Mozambique: Instituto Superior Pedagogico.
In this book, subtitled "Reflections on the tradition of sand drawings in Africa South of the Equator", Dr. Gerdes shows us many facets of an Ethnomathematics investigation. This volume analyzes and reconstructs mathematical knowledge in the tradition of sand drawings which are patterns of lines following geometric algorithms, embracing points of a reference grid. Particularly important are the use of only one line in these drawings and their other rules which are very much part of the tradition. A second volume is available which gives ideas for possible uses of Sona for mathematics education.

Gerdes, P. (1998). On possible uses of traditional Angolan sand drawings in the mathematics classroom. Educational Studies in Mathematics. 19, 3-22. Science (3rd) QA11.E3.

Gillings, R. J. (1982). Mathematics in the time of Pharaohs. Cambridge, MA: MIT Press. Science (3rd) QA27.E3G52.

Gittleman, A. (1975). History of mathematics. Columbus, OH: Charles E. Merrill Publishing Company.
In this work mathematics is shown as a part of human culture which is developed in response to environment, social stresses, and previous mathematics. Early history tends to be divided by culture, and then chronologically. The explanations given by the author are understandable and the solutions to problems are easy to follow. Indeed, there are many enjoyable anecdotes and cartoons.

Gow, J. (1968). A short history of Greek mathematics. NY: Ginn & Co.
This book was about the history of Greek mathematics. Ancient Greeks studied mathematics for its own sake rather than only because of its practical aspects. Greeks seemed to have an insatiable desire to know the true meaning of everything in the universe and to be able to give a rational explanation of it. This desire led the Greeks to many important discoveries in science in mathematics. From a scientific point of view, an advantage possessed by the Greeks was their remarkable capacity for accurate observation. Science (3rd) QA22.G7.

Grattan-Guinness, I. (Ed.) (1980). From the Calculus to Set Theory, 1630-1910. Rankine Road, Basingstoke, Hants. Taylor and Francis (Printers) Ltd.
This text gives the history of calculus. It also includes some of the important founders of calculus and how different topics were discovered. High School/ College, European, 1630 1910. Galin, Science (3rd) QA21. F77.
Grattan-Guinness, I. (Ed.) (1994). Companion encyclopedia of the history and philosophy of the mathematical sciences. New York: Routledge. Science (2nd) Reference QA21.C645 1994.

H


Heath, T. (1921). A history of Greek mathematics. Oxford: Clarendon Press.
Included in this book is a discussion on the beginnings of trigonometry. The works of Hipparchus, Menelaus, and Ptolemy are looked at in detail. Hipparchus used spherical trigonometry in his many astronomical investigations. He invested the motions of the sun, moon, and planets. He also compiled a catalogue of fixed stars in which he stated their positions and apparent sizes. Much of Hipparchus's work is lost to us, but we do have some of Ptolemy's work, which was based much on that of Hipparchus. Science (3rd) QA22.H438h.

Heath, T. L. (1931). A manual of Greek mathematics. Oxford: Carendon Press.
This book discusses Hipparchus's astronomical and geographical works. Hipparchus's systematic use of trigonometry is fairly conclusive. And we know about it mainly from Ptolemy. Ptolemy' s Syntaxis contains particulars of the observations and investigations carried out by Hipparchus, as well as of earlier observations recorded by him. Because Ptolemy based himself on Hipparchus, it is questionable whether Ptolemy contributed anything of great value except a definite theory of the motion of the five (then known) planets, which Hipparchus also studied. The mathematical interest of Ptolemy's work lies in his use of trigonometry. Science (3rd) QA22.H438m.

Hooper, A. (1948). Makers of mathematics. New York: Random House. Science (3rd) QA21.h785m.

Hoyrup, J. (1994). Babylonian mathematics. In I. Grattan-Guinness (Ed) Companion encyclopedia of the history of and philosophy of the mathematical Sciences. pp. 21-29. New York: Routledge.


J



Jacobs, H. (1970). Mathematics: A Human Endeavor: A book for those who think they don't like the subject. Englewood Cliffs, NJ: Prentice-Hall.
Chapter five deals with regular polygons and tesselations. This book is a rich source of enjoyable mathematics written to intrigue and instruct high school students and other interested readers. Science (3rd) QA93.J33.

Jacobs, H. (1972). Mathematics: A Human Endeavor.
Intended as alternative form of secondary-school textbook. Discussions on a basic level, related to standard curriculum with problems included, but all text is historically based. Athens Regional Library 510. (A newer version is available by San Francisco: W.H. Freeman, 1982 at Science (3rd) QA93.J33.

Johnson, Van L. (1969). The roman origins of our calendar. Medford, Massachusetts: American Classical League.
This book contains pictures of pieces of recovered Roman calendar. The author of this book, as I have found among other research, believes that we owe Rome, "who was our chief benefactor: not only did she bring together the various elements involved, fusing the science of the East with her own beliefs and universalizing both; but to her we owe so much in matters of linguistic and chronological detail, i. e. the names and order of the months, the distribution of days within the months, even to some extent the dating of Christian festivals like Christmas and Easter." Main (4th) CE46.J6.

K

Katz, V. (1993). A history of mathematics: An introduction. New York. Harper Collins College Publishing.
This text is similar to the first text. It is an introduction to the history of mathematics. It tells who, why, how, and when different mathematical topics were developed or discovered. It covers the Ancient to the modern. High School/ College, All Cultures, all times. Science (3rd) QA21.K33.

Kiracofe, R. (1993). The American quilt. New York, New York: Clarkson N. Potter.
A history of "cloth and comfort" from 1750 to 1950. The history of the United States is shown in quilting and its many facets . Even though this craft was not started in this country it quickly developed into an indigenous art form. Materials used and patterns designed were dictated by the environmental factors of daily life. The designs are quite imaginative and bold; most are geometric. Main (7th) NK9112.K57.

Kitroeff, A. (1989). The Greeks in Egypt, 1919-1937: Ethnicity and class. Atlantic Highlands, NJ: Ithaca Press.
Social classes and economic conditions of the Greeks in Egypt. Main (4th) DT155.2.G74K58.

Kline, M. (1959). Mathematics and the physical world. NY: Thomas Y. Crowell Company.
The aim of this text is to show the contributions of mathematics to the understanding of nature and the physical world. The author also wants to show the relationship between mathematics and the study of nature and the role that mathematics plays in the study of nature. High School/ College, All cultures, All times. Science (3rd) QA21.K65m.

Kline, M. (1972). Mathematical thought from ancient to modern times. NY: Oxford University Press.
This is volume 1 of a three volume set. This text looks at "the major mathematical creations and developments" from the ancient times to the beginning of the twentieth century. The aim of this text is to present the central ideas that have "loomed largest" in the main periods of mathematics. This book illustrates major mathematical developments from ancient times through the beginning of the 20th century. It emphasizes leading mathematical themes rather than men. This book is excellent in that it provides anecdotes and easy-to understand examples. High School/ College, All cultures, All times. Science (3rd) QA21.K516.

Krause, M. C. (1983). Multicultural mathematics materials. Long Beach, California: NCTM.
These activities and games are a collection from different parts of the world. Many have lasted through centuries. The materials have been tested in the classroom and are designed to bring the vitality of ethnic and cultural diversity to the study of mathematics. Science (3rd) QA16.K7 & Aderhold (2nd) Curr Mat Ctr Geography & History-Multicultur.

L

Libbrecht, U. (1973). Chinese mathematics in the thirteenth century. Cambridge, MA: The MIT Press. A lengthy book in the history of mathematics in China.
This book focuses on the thirteenth century. Added features are problems, reference table to problems, diagrams, and a glossary for terms. Science (3rd) QA27.C5L54.

Litchfield, P. C., Goldheim, D. A. & Dietrich, C. H. (1997). Euclid, Fibonacci, Sketchpad. Mathematics Teacher. 90 (1). pp. 8-12.
A new approach with GSP to an exercise which is found in most geometry textbooks in the form of a construction and is itself a variation of Proposition 10, Book 6 of Euclid's Elements: "to cut a given uncut straight line similarly to a given cut straight line. " In the process of figuring out the pattern for diving the line into unit fractions, the Fibonacci sequence appears. Main (2nd) LB1645.M4.

Lorch, R. (1995). Arabic mathematical sciences: Instruments, texts, transmission. Brookfield, VT: Variorum.
Focuses mostly on Arabic preservation, transmission, and adaptation of Greek mathematics. Also includes a good amount of discussion of astronomical sciences. Science 3rd QA27.A67L67.

M

Mahoney, M. S. (1973). The mathematical career of Pierre de Fermat. Princeton, NJ: Princeton University Press.
A biography and study of the work of the famous French mathematician, especially on his work with conic sections. Conic Sections. Science 3rd, QA29.F45M33.

Maor, E. (1994). e: The story of a number. Princeton, NJ: Princeton University Press.
The book describes the history of e from a human as well as a mathematical perspective, showing how a single number can tie together an entire period of mathematical history from the earliest seventeenth until the late nineteenth centuries, with the development of calculus at its center. It would be of interest to non-mathematicians as well as those already familiar with the number. Science (3rd) QA247.5.M33.

McCleary, J. & Rowe, D. E. (Ed.) (1989). The history of modern mathematics. New York: Academic Press, Inc.
Both volumes are proceedings of the Symposium on the History of Modern Mathematics held in 1989 at Vassar College. In Volume 1, Idea & Their Reception, the topics in math that are looked at include foundations of math, geometry, algebra, & many more. Volume 2, Institutions and Applications, looks at the different applications of math and how the developed. Science (3rd) QA21.S98.

Michalowicz, K. D. (1996). Fractions of ancient Egypt in the contemporary classroom. Mathematics Teaching in the Middle School. 1 (10). pp. 786-789.
Explanation to the Rhind Mathematical Papyrus. It shows students that mathematics is a human activity and aims at developing students' appreciation for ancient mathematics. Related References: Chace, Arnold Buffum. (1979). The Rhind Mathematical Papyrus. Reston, VA: NCTM. Gillings, Richard J. (1972). Mathematics in the Time of the Pharaohs. New York: Dover Publications. Aderhold (2nd) Curr Mat Ctr.

Michels, A. K. ( 1967). The calendar of the Roman republic. Princeton, NJ: Princeton University Press.
This book deals exclusively with the calendar of the Roman republic, commonly called the pre-Julian calendar. The author is very sharp to say that the book is about the Roman calendar, and that subject only. Not the evidence for religion or other Roman studies. Such things as the characters of the days, the history, and the dating of the calendar are included. Main (4th) CE46.M5.

Mikalson, J. D. (1975). The sacred and civil calendar of the Athenian year. Princeton, NJ: Princeton University Press.
Excellent material in this book! Information covering the use of calendars in ancient Greece as an attempt to systematize and regularize the celebration of religious festivals within the city-state. These calendars gave specific days and specific months for certain religious festivals and sacrifices to be held. Main (4th) CE42. M52.

Moffatt, M. (1977). The ages of mathematics: The origins.
This book is the first volume of four in the set. The series is intended to be a non-mathematical survey of the history of mathematics from its simplest beginnings. In this volume, the history of mathematics is traced from its primitive beginnings to the death of Hypatia. This book is very easy reading and could be enjoyed by students of all ages. Elementary/Middle/High School/ College, All Cultures. Athens Regional Library: 510 Ages.

Montague, H. F. (1963). The significance of mathematics. Columbus, Ohio: Charles E. Merrill Books.
A book about the meaning of and methods mathematics, this text was designed to emphasis the various roles of mathematics: a search for patterns including geometric, arithmetic, and new; a way of thinking; a part of our cultural heritage, and as a tool. Although designed for non-mathematically oriented students, it is nevertheless an interesting study for anyone. Science (3rd) QA93.M759s.

Monture, J. (1993). The complete guide to traditional Native American beadwork. New York, New York: Macmillan Publishing Co.
This guide covers all aspects of Indian beadwork including color, design, and history as well as complete directions for obtaining and using materials for this craft. Historical notes on the different Indian nations are included. This is truly an American art. Main (4th) E98.B46M66.

Morgan, V. M. (1990). Through the ages. New York, New York: Vantage Press, Inc. Here is a bird's eye view of the history of mathematics. Contributions to the various branches of mathematics as well as insights into the lives of those who made those contributions are presented in an interesting and readable way along with line drawing and related projects. Although the book is designed for middle school students, it would be of interest to higher grades also. Aderhold (2nd) Curr Mat Ctr PURE SCIENCES SECONDARY MATHEMATICS.

Motz, L. & Weaver, J. H. (1993). The story of mathematics. A discussion of the history of mathematics in novel format. Definitely written for the lay mathematician without much technical background. Athens Regional Library 510.9.

N

National Council of Teachers of Mathematics. (1969). Symmetry, congruence and similarity. Washington, DC: Author.
Booklet number eighteen in a series of topics in mathematics for elementary school teachers: This is an easy, brief introduction to the topics of symmetry, congruence and similarity. Because of its publication date, it is not very attractive. However, the information presented is accurate.

National Council of Teachers of Mathematics. (1969). Historical topics for the mathematics classroom. Washington, DC: Author.
This NCTM yearbook (#31). discusses the history of mathematics as a teaching tool, the history of numbers, numerals, computation, geometry, trigonometry, algebra, and calculus. The discussions are interesting and provide a wide variety of topics to select for use and further study. The material is extremely practical for teachers. Science (3rd) QA21.H559.

Neugebauer, O. A (1975). History of ancient mathematical astronomy.
This three-volume work is mostly about astronomy, but necessarily discusses a lot of early developments in trigonometry which were intimately related. Science 3rd QB16.N46.

Newman, J. R (1956). The world of mathematics. . New York: Simon and Schuster.
A neat collection of primary source documents reprinted collectively. Includes significant works by Bernoulli, Polya, Russell, Boole, etc. 4 volumes. Science (3rd) QA3.N6.

O

O'Shea, T. (1986). Dirichlet polygons: An example of geometry in geography. Mathematics Teacher. 79 (3)., pp. 170-173.
The purpose of this article is to outline an example of how geometry serves as a model in the real world and to suggest how it might be used at the high school level. The application involves the geography of human settlement. Although the article is interesting, it is rather technical reading. Main (2nd) LB1645.M4.

P

Pappas, T. (1986). Joy of mathematics. San Carlos, California: Wide World Publishing/Tetra .
The author's plan is to reveal the influence and nature of mathematics around us on a daily basis. It appears in nature, art, music, architecture, the sciences, and literature. Many of the sections in this interesting paperback have the history of the particular problem included quite nicely in the section. Of particular historical interest are the parts dealing with "a twist to the Pythagorean theorem" which involves a proof with parallelograms, the quipu, the evolution of mathematical ideas, tessellations, and Moslem art. Aderhold (2nd) Curr Mat Ctr Pure Sciences-2nd Math.
Parkinson, C. L. (1985). Breakthroughs: A Chronology of Science. Boston, MA: G.K. Hall. Science (3rd) Q125.P327.

Perl, T. (1978). Math equals: Biographies of women mathematicians and related activities. Menlow Park, CA: Addison-Wesley.
Pages 83-101 contain biographical information on Mary Fairfax Somerville. As part of her research, she investigated Chladni diagrams and the symmetry of nodal lines created when surfaces vibrate. Science (3rd) QA28.P47.

Phillips, E. (1987). Studies in the history of mathematics. Washington, D.C. : Mathematical Association. Science (3rd) QA21.S92.

Pomeroy, S. (1984). Women in Hellenistic Egypt: From Alexander to Cleopatra. New York: Schocken Books Main (5th) HQ1137.E3P65.

Ptolemy, C. (1985). The Almagest. Translated and annotated by G.J. Toomer. New York: Springer-Verlag. Science (3rd) QB41.P957.

R


Robins, G. , and Shute, C. (1987). The Rhind mathematical papyrus: an ancient Egyptian Text. New York: Dover Publications.

S

Sachs, L. (1988). Projects to enrich school mathematics. Reston, VA: NCTM.
Sixteen teachers have each written a challenging research project for secondary school level on topics that do not often receive in-depth study. The independent projects include suggestions for work on tessellations, Pi and its history, transformations and matrices with applications, Pythagoras and his theorem, Pascal and his triangle, and more. Aderhold (2nd) Curr Mat Ctr Pure Sciences-Math Activities.

Salzman, M. R. (1990). On Roman time: The codex-calendar of 354 and the rhythms of urban life in late antiquity. Berkeley, CA: University of California Press.
An attempt to give instruction and explain how the functions of the Roman calendar worked. . what purposes did they serve, etc. The Codex-Calendar of 354 AD is the only calendar that has survived in its entirety from the time of the Roman Empire. This calendar allows us to look into the society that produced it. Aspects of daily life and institutions that are otherwise lost to us. Main (4th) CE46.S25.

Samuel, A. E. (1972). Greek and Roman chronology. Ser. 1 Sect. 7. Munchen: Beck.
This book goes over the background of the sun-earth-moon system, the construction of calendars, Greek Astronomical calendars, civil calendars, calendars of the Hellenistic Kingdoms, etc. Main (3rd) PA25.H24.

Sarton, G. (1957). The study of the history of mathematics and the study of the history of science. New York, NY: Dover Publications.
The history surrounding the development of mathematics and science. History of mathematics. Science 3rd, QA21.S251.

Schmalz, R. (1993). "Out of the mouths of mathematicians": A quotation book for philomaths. Washington, D.C.: Mathematical Association of America.
Most of the quotes in this delightful volume are from mathematicians from the twentieth century; the passages are included on the basis of the fame of the writer, the merit of the message, and the style of expression. Some of sections included are: "Mathematics in General", "Moments of Mathematical Insight", "Mathematics and Matters of the Spirit", "Anecdotes and Miscellaneous Humor", and "Mathematics Education." Science (3rd) QA99.S25.

Scott, J. F. (1960). A history of mathematics ,from antiquity to the beginning of the nineteenth century. London: Taylor & Francis.
This book discussed how the science of trigonometry began. It is mentioned in the book that the Egyptians probably knew that the different elements of a triangle were in some way related; but the focus is on Greeks, who established precise relations between its sides and angles. It was with the astronomical calculations that trigonometry came to be invented. Because of this, the study of spherical trigonometry proceeded that of plane. Many of the early trigonometric rules that were developed are in the Almagest, a book written by the Greek mathematician Claudius Ptolemy. Science (3rd) QA21.S4.

Serra, M. (1993). Discovering geometry. An inductive approach. Berkeley, CA: Key Curriculum Press.
An exciting geometry book? Is it possible? It appears it may be. The students are urged to have fun while they learn. There are many interesting hands on projects, both individual and group. The first chapter is entitled Geometric Art and the first illustration in the book is by M. C. Escher. A later chapter on Transformations and Tessellations includes properties of symmetry and reflection. After months of working with geometry inductively, the author includes deductive reasoning and geometric proof at the end of the book. In this way students do not have to learn proof techniques until they understand the shapes and reasoning involved.

Seymour, D. (1989). Introduction to tessellations. Palo Alto, California: Dale Seymour Publications.
A resource with hundreds of detailed graphic illustrations, this book ranges from the simplest fundamental concepts to the intricate and exacting procedures of creating designs like those of M. C. Escher. Among the topics are properties of tessellating polygons, regular and semiregular tessellations, and star polygons of Islamic art as well step-by-step visual demonstrations of exactly how tessellations are created. There is a companion volume, Tessellation Teaching Masters which may be of interest particularly to middle school and higher teachers. Aderhold (2nd) Curr Mat Ctr.

Shirley, L. H. (1996). Activities from African calendar and time customs. Mathematics Teaching in the Middle School. 1, (8). pp. 616-620. Mathematics in a wider range of applications and cultures than in the past.: African day-names, the sunrise clock, the Islamic calendar. Aderhold (2nd) Curr Mat Ctr.

Smith, D. E. (1925). History of mathematics. NY: Ginn & Co.
History of Mathematics Trigonometry as we know it began around the 17th century. However, if we take trigonometry to mean the mathematics used to study astronomy which used certain functions of angles, its origin may be in the works of Hipparchus (around 140 BC). If we took trigonometry to simply mean angle measurement (as its literal meaning suggests) then its origin is even earlier. The study of astronomy and the unraveling of the mysteries of the universe, led to the study of the celestial sphere. This accounts for the fact that Greek trigonometry focused on spherical triangles. The first evidence of the study of spherical triangles is in Menelaus' s work on spherics. Science (3rd) QA21.S645h.

Smith, S. (1996). Agnesi to Zeno. Berkeley, California: Key Curriculum Press.
M. C. Escher: Artist and Geometer is one of the over one hundred vignettes presented in this book. The page following the vignette includes several activities to be used with high school/middle school students as well as related readings.

Smoothey, M. (1993). Let's investigate shape patterns. North Baltimore, NY: Marshall Cavendish Corporation.
This book geared to juveniles explores the world of shapes and how they can be drawn. Triangular and square dotted grids are available for copying for the many projects included. Included in this list are pentominoes, lines of symmetry, mirror codes, reflections without drawing, finding lines of symmetry, tiling with quadrilaterals, and tessellating with other shapes.

Spence, B. S. (1991). Multicultural mathematics education for the middle grades. Arithmetic Teacher 38, 8-13. Main (2nd) LB1589.A7.

Spence, B. S. (1996). The arcs of archaeology. Mathematics Teaching in the Middle School. 1, (9). pp. 668-693.
This article explains to students that mathematics is not isolated from other subject. It also shows students how mathematics is used in the real world. Aderhold (2nd) Curr Mat Ctr.

Stemberg, S. (1970). Studies in Hebrew astronomy and mathematics. New York: Ktav Publication House.
This book is a collection of papers dealing with the history of Jewish astronomy and mathematics. The author relates Jewish law and tradition to the development of Hebrew astronomy and mathematics. Original Hebrew passages in the book would make this good reading for a Hebrew scholar. High School College, Hebrew. Science (3rd) QB34.G35.

Struik, D. J. (1987). A concise history of mathematics (4th Ed). New York, NY: Dover Publications.
This is a good chronological history from the Old Stone Age to the first half of the 20th Century. Historical and Cultural events are highlighted with particular emphasis given to mathematicians and the problems they posed. Science (3rd) QA21.S87.
Bray, W., Swanson, E., & Farrington, I. S. (1975). The New World; the making of the past. Oxford: Elsevier. Main (4th) E61.B824.

Swetz, F. (1992). The Sea Island mathematical manual. University Park PA: Pennsylvania State University.
This book is about mathematics and surveying in ancient China. Interesting features included are the drawings and diagrams. Also included is a glossary to help with difficult terms. Science (3rd) TA527.C6S94.

T

Tahan, M. (1972). The man who counted. A collection of mathematical adventures. New York: W. W. Norton and Co. , Inc.
The adventures of Beremiz Samir, The Man Who Counted, take the reader on an exotic journey in which, time and again, he summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame, fortune, and rich rewards. One learns much of the history of famous mathematicians who preceded him, seems to undergo a series of trials at the hands of the wise men of the day, and comes to admire Beremiz' warm wisdom, patience, and astute solving of problems. These stories are delightful.

Tannenbaum, P. (1995). Excursions in modern mathematics. Englewood Cliffs, NJ: Prentice-Hall.
There is more history in this modern college-level text for liberal arts major than one might expect. It is worked in with the concepts quite easily and does not seem to hinder the emphasis on modern techniques some of which have been developed within the last twenty years. Applications are very important in this book and although many of the problem are imaginary they are certainly possible. A fine section on symmetry, reflection, and tessellation is included. Science (3rd) QA36.T35.
Turnbull, H. (1962). The great mathematicians. New York: Simon and Schuster. Science (3rd) QA28.T942g.

W

van de Waerden, B. L (1983). Geometry and algebra in ancient civilizations. New York: New York: Springer-Verlag. Science (3rd) QA151.W34.

Welchons, A. M. (1949). Plane geometry. Boston, MA: Ginn and Company.
A book which is old enough to be used to demonstrate the history of teaching plane geometry in this country has even older history worked into its text in a natural and easily understood way. The introduction includes not only an overview of the history of plane geometry but a section on solid geometry. Other comments are included in the text, sometimes right along with an explanation of the proofs. For instance, when the Pythagorean theorem is presented, it not only mentions that his method of demonstration is not known and the proof given here is attributed to Euclid, but it also outlines the demonstration of the theorem devised by President Garfield.

Whitman, N. (1991). Line and rotational symmetry. Mathematics Teacher, 84 (4). pp. 296-298.
An activity for grades 5-10 designed to demonstrate the concepts of line and rotational symmetry using a physical model and Hawaiian quilt patterns. Main (2nd) LB1645.M4.

Y


Yan, Li & Shiran, Du (1987). Chinese mathematics: a concise history. Oxford, England: Clarendon Press.
The co-authors did an outstanding job presenting ideas and topics from Chinese mathematics. Moreover, one could readily see the many contributions of the Chinese to the mathematics of today. Science (3rd) QA27.C5L4713.

Z

Zaslavsky, C. (1973). Africa Counts. New York: Lawrence Hill Books.
Described here for the first time is the contribution of African peoples to the science of mathematics. Using numbers and patterns as organizing principles, Ms. Zaslavsky describes the numeration systems - some of them highly complex - the mystical attributes of numbers, geometry in art and architecture and mathematical games, all of which reveal a highly developed understanding of mathematics. She uses photographs, graphs, diagrams, personal anecdotes and quotations from African literature and oral tradition to document this important contribution to a hitherto little-known aspect of African culture." Main (6th) GN476.1.Z37.

Zaslavsky, C. (1989). People who live in round houses. Arithmetic Teacher 37 pp. 18-21. Main (2nd) LB1589.A7.