Article
Full entry |
PDF
(2.2 MB)
Feedback
PDF
(2.2 MB)
Feedback
Summary:
The general geometric transformations between the general concurrent charts of three variables and the general tangential contact charts of three variables are researched in this paper. General geometric transformations treated here are of the form: $u(x,y)\bar{x}+v(x,y)\bar{y}+w(x,y)=0$, by which the general concurrent charts in $(x,y)$-plane and the general tangential contact charts in $(\bar{x},\bar{y})$-plane are transformed to cach other, by the envelope method or the contact transformation method.
References:
[1] Bal L.: Quelques Types de Nomogrammes Tangentiels. Mathematica, Vol. 2 (25), No. 2, 1960, pp. 201 - 210. MR 0135244 | Zbl 0104.35402
[2] Otto E.: Nomography. Pergamon Press, Oxford, 1963, pp. 169-174. MR 0158570 | Zbl 0108.13104
[3] Йокл E.: Составные номограммы с ориентированным транспарантом и из выравненных точек, в которых используются контакты касания. Номографический сборник, № 4, M., ВЧ АН СССР. 1967, 135-146. Zbl 1103.35360
[4] Morita K., and Sató О.: A Method of Constructing General Contact Tangential Charts. Aplikace matematiky, 18 (1973), 238 - 248. MR 0317568
[5] Klein F.: Elementarmathematik vom höheren Standpunkte aus. dritte Aufl., Zweite Bd., Julius Springer, Berlin, 1925, S. 117-119.
[6] Záhora J.: Nomogramy adjungované k dotykovým a průsečíkovým nomogramům majícím aspoň jeden systém křivých isoplét. Aplikace matematiky, 14 (1969), 195 -209. MR 0242401
[7] Záhora J.: Dotykové nomogramy s kružnicemi. Nomografický zborník [Zborník prednášok III. celoštátnej konferencie o nomografii], VŠT-Košice, Sep. 23 -25, 1970, 215 -230.
[8] Woods F. S.: Higher Geometry. Dover Publications, Inc., New York, 1961, 131 - 132. MR 0124784 | Zbl 0098.12901
[9] Schwerdt H.: Lehrbuch der Nomographie. Julius Springer, Berlin, 1924, 219--240.
[10] Cohen A.: An Introduction to the Lie Theory of One-Parameter Groups. G. E. Stechert & Co., New York, 1931, 178-185.
[11] Adams D. P.: Nomography - Theory and Applications. Archon Books, Hamden, Connecticut, 1964, 153-172.
Search
Partner of
