University of Texas at Austin
Who did G. B. Halsted work for from 1884 to 1902?
G . B . Halsted George Bruce Halsted ( November 25 , 1853 – March 16 , 1922 ) , usually cited as G . B . Halsted , was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and his many important translations . Especially noteworthy were his translations and commentaries relating to non-Euclidean geometry , including works by Bolyai , Lobachevski , Saccheri , and Poincaré . He wrote an elementary geometry text , Rational Geometry , based on Hilberts axioms , which was translated into French , German , and Japanese . Life . Halsted was a tutor and instructor at Princeton University . He held a mathematical fellowship while a student at Princeton . Halsted was a fourth generation Princeton graduate , earning his bachelors degree in 1875 and his Masters in 1878 . He went on to Johns Hopkins University where he was J . J . Sylvesters first student , receiving his Ph.D . in 1879 . After graduation , Halsted served as an instructor in mathematics at Princeton until beginning his post at the University of Texas at Austin in 1884 . From 1884 to 1903 , Halsted was a member of the University of Texas at Austin Department of Pure and Applied Mathematics , eventually becoming its chair . He taught mathematicians R . L . Moore and L . E . Dickson , among other students , who frequently joked that his primary criterion for the rationality of a geometric system was the simplicity of the terms in which it could express the closed space figure formed by the contours of his mustache . He explored the foundations of geometry and explored many alternatives to Euclids development , culminating with his Rational Geometry . In the interest of hyperbolic geometry in 1891 he translated the work of Nicolai Lobachevsky on theory of parallels . In 1893 in Chicago , Halsted read a paper Some salient points in the history of non-Euclidean and hyper-spaces at the International Mathematical Congress held in connection with the Worlds Columbian Exposition . Halsted frequently contributed to the early American Mathematical Monthly . In one article he championed the role of J . Bolyai in the development of non-Euclidean geometry and criticized C . F . Gauss . See also on 3 September 1912 . In 1903 , Halsted was fired from UT Austin after having published several articles that criticized the university for having passed over R . L . Moore , at that time a young and promising mathematician whom Halsted hoped to have as an assistant , for an instructor post in favor of a well-connected but less qualified candidate with roots in the area . He completed his teaching career at St . Johns College , Annapolis ; Kenyon College , Gambier , Ohio ( 1903-1906 ) ; and the Colorado State Teachers College , Greeley ( 1906-1914 ) . Halsted was a member of the American Mathematical Society and served as vice president of the American Association for the Advancement of Science . He was elected Fellow of the Royal Astronomical Society in 1905 . Synthetic projective geometry . In 1896 Halsted published a chapter on synthetic geometry pertaining to three-dimensional projective geometry in Higher Mathematics distributed by Mansfield Merriman and Robert S . Woodward . In 1906 Synthetic Projective Geometry was published separately in 241 articles and 61 problems . A bibliography referring to Chasles , Steiner , and Clebsch appears on page 24 . There are four pages of index , 58 of text , and a lyrical preface : “Man imprisioned in a little body , with short-arm hands instead of wings , created for his guidance a mole geometry , tactile space , codified by Euclid in his immortal Elements , whose basal principle is congruence , measurement . Yet man is no mole . Infinite feelers radiate from the windows of his soul , whose wings touch the fixed stars . The angel of light in him created for the guidance of eye-life an independent system , a radiant geometry , a visual space , codified in 1847 by a new Euclid , by the Erlangen professor , George von Staudt , in his immortal Geometrie der Lage , published in the quaint and ancient Nurnberg of Albrecht Durer.” By developing concepts of eject and cut , the text relates abstraction to practice in perspective drawing or a picture plane ( page 10 ) . A line is called a straight and includes a figurative point . Halsted uses the approach of a Steiner conic in article 77 for the definition of a conic : “If two coplanar non-copunctual flat pencils are projective but not perspective , the crosses of correlated straights form a range of the second degree’ or ‘conic range’ . The eject of a conic is a cone , while the cut of a cone is a conic’ . Since four arbitrary points in a plane have six connectors , there are three more points determined by the crosses of the connectors . Halted calls the original four points dots and the extra three codots . Standard nomenclature refers to the configuration as a complete quadrangle while Halsted says tetrastim . Each codot corresponds to a pair of opposite connectors . Four harmonic points are defined “if the first and third are codots of a tetrastim while the others are on the connectors of the third codot” ( pages 15 , 16 ) . For a given conic C , a point Z has a corresponding straight the polar of Z and Z is the pole of this straight : Through Z draw two secants through C crossing at AD and BC . Consider the tetrastim ABCD which has Z as a codot . Then the polar of Z is the straight through the other two codots of ABCD ( page 25 ) . Continuing with conics , conjugate diameters are straights , each of which is the polar of the figurative point of the other ( page 32 ) . Publications . - Metrical geometry ; An elementary treatise on mensuration ( Boston , Ginn , 1890 ) , link from Internet Archive . - The Elements of Geometry ( New York , Wiley , 1889 ) , @ Internet Archive . - Elementary Synthetic Geometry ( New York , Wiley , 1896 ) @ Internet Archive - ( translation ) : New Principles of Geometry with a Complete Theory of Parallels by Lobachevsky , ( Austin , Neomon , 1897 ) link from Yale University - Synthetic Projective Geometry ( New York , Wiley , 1906 ) , @ Internet Archive . - On the Foundation and Technic of Arithmetic ( Chicago , Open Court , 1912 ) , @ Internet Archive .