| Title:
|
A generalization of the Holditch theorem for the planar homothetic motions (English) |
| Author:
|
Yüce, Salim |
| Author:
|
Kuruoğlu, Nuri |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
87-91 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves. (English) |
| Keyword:
|
Steiner formula |
| Keyword:
|
Holditch Theorem |
| Keyword:
|
homothetic motion |
| MSC:
|
53A17 |
| idZBL:
|
Zbl 1099.53009 |
| idMR:
|
MR2125151 |
| DOI:
|
10.1007/s10492-005-0005-3 |
| . |
| Date available:
|
2009-09-22T18:20:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134593 |
| . |
| Reference:
|
[1] A. Broman: Holditch’s theorem is somewhat deeper than Holditch thought in 1858.Normat 3 (1979), 89–100. Zbl 0415.53003, MR 0548827 |
| Reference:
|
[2] A. Broman: Holditch’s theorem.Math. Mag. 54 (1981), 99–108. Zbl 0468.51005, MR 0618595, 10.2307/2689793 |
| Reference:
|
[3] A. Tutar, N. Kuruoğlu: The Steiner formula and the Holditch theorem for the homothetic motions on the planar kinematics.Mech. Mach. Theory 34 (1999), 1–6. MR 1738623, 10.1016/S0094-114X(98)00028-7 |
| Reference:
|
[4] H. Holditch: Geometrical theorem.Q. J. Pure Appl. Math. 2 (1858), 38–39. |
| Reference:
|
[5] H. R. Müller: Erweiterung des Satzes von Holditch für geschlossene Raumkurven.Abh. Braunschw. Wiss. Ges. 31 (1980), 129–135. (German) MR 0608278 |
| Reference:
|
[6] H. Pottmann: Holditch-Sicheln.Arch. Math. 44 (1985), 373–378. Zbl 0542.53008, MR 0788954 |
| Reference:
|
[7] H. Pottmann: Zum Satz von Holditch in der euklidischen Ebene.Elem. Math. 41 (1986), 1–6. Zbl 0584.53005, MR 0880237 |
| Reference:
|
[8] J. Hoschek: Eine Verallgemeinerung des Satzes von Holditch.Monatsh. Math. 80 (1975), 93–99. Zbl 0318.53015, MR 0400071, 10.1007/BF01339077 |
| Reference:
|
[9] L. Hering: Sätze vom Holditch-Typ für ebene Kurven.Elem. Math. 38 (1983), 39–49. (German) Zbl 0468.53002, MR 0700282 |
| Reference:
|
[10] M. Spivak: Calculus on Manifolds. A modern approach to classical theorems of advanced calculus.W. A. Benjamin, New York, 1965. Zbl 0141.05403, MR 0209411 |
| Reference:
|
[11] N. Kuruoğlu, S. Yüce: The generalized Holditch theorem for the homothetic motions on the planar kinematics.Czechoslovak Math. J. 54(129) (2004), 337–340. MR 2059254, 10.1023/B:CMAJ.0000042372.51882.a6 |
| Reference:
|
[12] S. Hentschke: Erweiterungen des Satzes von Holditch.Sitzungsber. Österr. Akad. Wiss. 184 (1975), 451–458. (German) MR 0436011 |
| Reference:
|
[13] W. Blaschke, H. R. Müller: Ebene Kinematik.Verlag Oldenbourg, München, 1956. (German) MR 0078790 |
| . |
