Background
Ernest Julius Wilczynski was born on November 13, 1876 in Hamburg, Germany, the son of Max and Friederike (Hurwitz) Wilczynski. His family emigrated to America while he was still quite young, and settled in Chicago, Ill.
(Projective Differential Geometry of Curves andR uled Surf...)
Projective Differential Geometry of Curves andR uled Surfaces was written byE rnest Julius Wilczynski in 1906. This is a 306 page book, containing 103100 words and 4pictures. Search Inside is enabled for this title. (Typographical errors above are due to OCR software and don't occur in the book.) About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology. Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...by Cayley, in 1859, who showed that by means of them it becomes possible to characterize a space-curve analytically, by means of a single equation. To Cayley, also, is due the quadratic relation between the six homogeneous line-coordinates. We repeat the definition. Let yu...yt and zl,... zi be two points of the line. Put (1) (oik = yiZk--ykZi 0, & = 1,2,3,4). Since mn = 0, and to,-=--ra,-, we need retain only six of these quantities, say li' ral3, mU, Sf m4t2, mw We define these to be the six homogeneous coordinates of the line. The propriety of this definition has already been explained. There is a one-to-one correspondence between the lines of space and the ratios of the above six quantities. There is, of course, a relation between these six quantities, since there are not oo5, but only oo lines in space. This relation has already been found to be (cf. Chapter II, § 6), (2) SI = rali a3i + a13 ra42 + rau an = 0, where £1 may be used as an abbreviation for the left member. Conversely any six quantities which satisfy (2) may be interpreted as homogeneous coordinates of a line. It is easy to see that, corresponding to any projective transformation of space, the six homogeneous line-coordinates ral undergo a homogeneous linear substitution which, of course, leaves (2) invariant. A line may be determined as the intersection of two planes, instead of being considered as joining two points. If uu... M4 and v1,...vi are the coordinates of two planes which contain the line, the determinants ik = uivk--ukvi may also be defined as coordinates of the line. These new coordinates tik are defined in a fashion dual to the definition of the first set to.-, and line-geometry is clearly a self-dual field, its element being self-dual. As a consequence of this ...
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Ernest Julius Wilczynski was born on November 13, 1876 in Hamburg, Germany, the son of Max and Friederike (Hurwitz) Wilczynski. His family emigrated to America while he was still quite young, and settled in Chicago, Ill.
He attended elementary school and high school in Chicago and, with the assistance of an uncle, returned to Germany to enter the University of Berlin, where he received the degree of Ph. D. in 1897. He was then in his twenty-first year.
After his return to the United States he was a computer in the office of the Nautical Almanac in 1898, and then he was appointed instructor in mathematics at the University of California. Here he remained as assistant and associate professor until 1907, with the exception of the period from 1903 to 1905 when he was in Europe as a research associate of the Carnegie Institution of Washington. He was associate professor of mathematics at the University of Illinois from 1907 to 1910 and at the University of Chicago from 1910 to 1914. He was made professor of mathematics at Chicago in 1914 and, after his health failed, professor emeritus in 1926. His death came at Denver, Col. , after a lingering illness of about nine years. Most of this time he was confined to his bed, but he never gave up hope of some day returning to his academic duties. He began his scientific career as a mathematical astronomer and his interest then turned to differential equations, but he attained eminence as a projective differential geometer. This field of geometry was largely created by him. He was lecturer at the New Haven Colloquium of the American Mathematical Society in 1906 with E. H. Moore and Max Mason. He was vice-president of the American Mathematical Society, and a member of the council of the Mathematical Association of America. In 1909 he won a prize of the Royal Belgian Academy of Sciences for an original paper in geometry, and he was elected a member of the National Academy of Sciences in 1919. He was also a fellow of the American Association for the Advancement of Science. One of Wilczynski's primary accomplishments was his mastery of the difficult art of lucid mathematical exposition.
(This book was originally published prior to 1923, and rep...)
( This work has been selected by scholars as being cultur...)
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(Projective Differential Geometry of Curves andR uled Surf...)
(This is a pre-1923 historical reproduction that was curat...)
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(This is an EXACT reproduction of a book published before ...)
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He possessed a fine and polished style both in spoken and written English and in German, his native language. He was familiar with French and Italian. His lectures, clear and concise, were greatly admired by his students.
He was married to Countess Inez Macola of Verona, Italy, on August 9, 1906. She, with their three daughters, survived him.