Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

被引：1
|
作者：
Yuce, Salim [1 ]
Kuruoglu, Nuri [2 ]
机构：
[1] Yildiz Tech Univ, Fac Arts & Sci, Dept Math, TR-34210 Istanbul, Turkey
[2] Univ Bahcesehir, Fac Arts & Sci, Dept Math & Comp Sci, TR-34100 Istanbul, Turkey
来源：
ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2009年 / 19卷 / 01期
关键词：
Holditch Theorem; hyperbolic motion; hyperbolic numbers;
D O I：
10.1007/s00006-008-0131-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 7] were expressed by H.R. Muller [9] under the one-parameter closed planar motions in the complex sense. In this paper, in analogy with complex motions as given by Muller [9], the Steiner formula and the mixture area formula are obtained under one parameter hyperbolic motions. Also Holditch theorems were expressed in the hyperbolic sense.
引用
收藏
页码：155 / 160
页数：6
相关论文
共 50 条
  • [21] On Holditch’s theorem
    Waldemar Cieślak
    Horst Martini
    Witold Mozgawa
    [J]. Journal of Geometry, 2020, 111
  • [22] The Steiner Formulas For The Open Planar Homothetic Motions
    Yuce, Salim
    Kuruoglu, Nuri
    [J]. APPLIED MATHEMATICS E-NOTES, 2006, 6 : 26 - 32
  • [23] On Holditch's theorem
    Cieslak, Waldemar
    Martini, Horst
    Mozgawa, Witold
    [J]. JOURNAL OF GEOMETRY, 2020, 111 (02)
  • [24] GENERALIZATION OF HOLDITCH THEOREM
    HOSCHEK, J
    [J]. MONATSHEFTE FUR MATHEMATIK, 1975, 80 (02): : 93 - 99
  • [25] The Holditch Sickles For The Open Homothetic Motions
    Yuce, Salim
    Kuruoglu, Nuri
    [J]. APPLIED MATHEMATICS E-NOTES, 2007, 7 : 175 - 178
  • [26] Unitarization and Inversion Formula for the Radon Transform for Hyperbolic Motions
    Bartolucci, Francesca
    Monti, Matteo
    [J]. 2019 13TH INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), 2019,
  • [27] GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS
    N.Kuruo(g|ˇ)lu
    M.Düldül
    A.Tutar
    [J]. Applied Mathematics and Mechanics(English Edition), 2003, (08) : 945 - 949
  • [28] The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C-p
    Erisir, Tulay
    Gungor, Mehmet Ali
    [J]. INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2018, 11 (02): : 111 - 119
  • [29] The generalization of Holditch theorem for closed space curves
    Düldül, M
    Kuruoglu, N
    Tutar, A
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2004, 84 (01): : 60 - 64
  • [30] Holditch's Theorem in 3D Space
    Monterde, Juan
    Rochera, David
    [J]. RESULTS IN MATHEMATICS, 2019, 74 (03)
12345