Howard Whitley Eves (10 January 1911, New Jersey – 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics.
Eves received his B.S. from the University of Virginia, the M.A. from Harvard University, and Ph.D. in mathematics from Oregon State University in 1948, the last with a dissertation entitled A Class of Projective Space Curves written under Ingomar Hostetter. He then spent most of his career at the University of Maine, 1954–1976. In later life, he occasionally taught at University of Central Florida.
Eves was a strong spokesman for the Mathematical Association of America, which he joined in 1942, and whose Northeast Section he founded. For 25 years he edited the Elementary Problems section of the American Mathematical Monthly . He solved over 300 problems proposed in various mathematical journals. His six volume Mathematical Circles series, collecting humorous and interesting anecdotes about mathematicians, was recently reprinted by the MAA, who also published his two volume Great Moments in the History of Mathematics, and his autobiographical Mathematical Reminiscences in 2001.
Eves had six children.
Alexander Grothendieck was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.
August Ferdinand Möbius was a German mathematician and theoretical astronomer.
The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Robert Daniel Carmichael was an American mathematician.
Marjorie Rice was an American amateur mathematician most famous for her discoveries in geometry. Rice was born in St. Petersburg, Florida, and died in California, where she lived with her son and daughter-in-law.
In Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions with additional restrictions. This result states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given.
Donald Clayton Spencer was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the University of Colorado and MIT.
Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger, and originally published in 1962 as Volume 13 of the Mathematical Expositions series of the University of Toronto Press. A corrected edition was published in 1979 in the Dover Books on Advanced Mathematics series of Dover Publications (ISBN 0-486-63830-8). The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Shlomo Zvi Sternberg, is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory.
Howard Jerome Keisler is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.
In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD.
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover.
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play.
Gary Theodore Chartrand is an American-born mathematician who specializes in graph theory. He is known for his textbooks on introductory graph theory and for the concept of a highly irregular graph.
Zeev Nehari was a mathematician who worked on Complex Analysis, Univalent Functions Theory and Differential and Integral Equations. He was student of Michael (Mihály) Fekete. The Nehari manifold is named after him.
In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation. The circle has the property that the solutions of the quadratic equation are the horizontal coordinates of the intersections of the circle with the horizontal axis. Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons.
Doris J. Schattschneider is an American mathematician, a retired professor of mathematics at Moravian College. She is known for writing about tessellations and about the art of M. C. Escher, for helping Martin Gardner validate and popularize the pentagon tiling discoveries of amateur mathematician Marjorie Rice, and for co-directing with Eugene Klotz the project that developed The Geometer's Sketchpad.
Richard Lawrence Bishop is an American mathematician, a professor emeritus of mathematics at the University of Illinois at Urbana–Champaign. The Bishop–Gromov inequality in Riemannian geometry is named after him.