During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…

This article traces the history of zero and its dual role as a placeholder, albeit of empty space, and as a number for computational purposes. The use of one symbol for both situations is shown to be tied to the adoption, and subsequent promulgation, of our modern numbering system. (JJK)

Discusses Napoleon's involvement with mathematics and education. Describes two geometric constructions dividing the circumference of a circle into four equal parts and finding the center of a given circle. Summarizes the establishment of the Institute of Egypt and the educational system in France. Twenty-seven references are listed. (YP)

Discoveries of Charles Babbage in the 1800s are described. Origins of the difference engine, his calculating machine, the principles of computation applied to tables, and the design and construction of his engine are included. (MNS)

Geometry is revealed as one of the most universal and useful tools in all parts of mathematics, with the idea of a "pure" geometry divorced from algebra an historically recent idea. (MP)

Pays homage to Freudenthal, a man who knew no cultural boundaries and who opposed obscurantism. His thoughts and works went in many complementary directions--mathematics, history of mathematics, mathematics education, and philosophy. He opened mathematics education to everyone and never lost the intellectual requirements of a great scientific…

A brief history of Amalie Emmy Noether is presented, citing many of her contributions to mathematics and physics. Major credit for the development of modern algebra should probably be given to her. Reference is made to Noether's theorem and Noetherian Rings. (MP)

This textbook covers geometry and trigonometry and presents problems for student consideration. Geometry principles are applied to surface and solid measurement. Tables of logarithms and logarithmic sines are included. [This book was translated from the French of A. M. Legendre. It was revised and abridged by Charles Davies.]

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

Briefly traces the development of computers from the abacus, John Napier's logarithms, the first computer/calculator (known as the Differential Engine), the first computer programming via steel punched cards, the electrical analog computer, electronic digital computer, and the transistor to the microchip of today's computers. (MBR)

Examines historically nine women mathematicians who are known and discusses some of their professional obstacles, including lack of educational and employment opportunities. Discusses the importance of mentors and sponsors and suggests girls should be made aware of the contributions of women mathematicians and their own potential. (JAC)

Schools exist to educate; school mathematics is, therefore, subject to particular forces that decisively distinguish it from mathematics as a scientific discipline. How educators in Germany in the early 19th century solved the problem of the relationship of school mathematics and its respective scientific discipline, i.e., scientific mathematics,…

This textbook is designed to be used in a geometry course incorporating the writings of Euclid. The object of this edition now offered to the public, is not so much to give the writings of Euclid the form which they originally had, as that which may at present render them most useful. The author believes that the use of algebraic signs and…

This textbook is a course in surveying. Geometry, land surveying, chain surveying, plain-table surveying, theodolite surveying, hilly-ground surveying, laying out land, division of land, and levelling are covered.

This work is chiefly a compilation from other books; and but very little new is added except a more full explanation, than has yet been published, of rectangular surveying, or the method of calculating the area of fields arithmetically, without drawing a plot of them and measuring with a scale and dividers, as has been the common practice; and…