A generalization of the Holditch theorem for the planar homothetic motions

Salim Yüce; Nuri Kuruoğlu

Applications of Mathematics (2005)

  • Volume: 50, Issue: 2, page 87-91
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Yüce, Salim, and Kuruoğlu, Nuri. "A generalization of the Holditch theorem for the planar homothetic motions." Applications of Mathematics 50.2 (2005): 87-91. <http://eudml.org/doc/33208>.

@article{Yüce2005,
abstract = {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.},
author = {Yüce, Salim, Kuruoğlu, Nuri},
journal = {Applications of Mathematics},
keywords = {Steiner formula; Holditch Theorem; homothetic motion; Steiner formula; Holditch Theorem; homothetic motion},
language = {eng},
number = {2},
pages = {87-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalization of the Holditch theorem for the planar homothetic motions},
url = {http://eudml.org/doc/33208},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Yüce, Salim
AU - Kuruoğlu, Nuri
TI - A generalization of the Holditch theorem for the planar homothetic motions
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 87
EP - 91
AB - 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.
LA - eng
KW - Steiner formula; Holditch Theorem; homothetic motion; Steiner formula; Holditch Theorem; homothetic motion
UR - http://eudml.org/doc/33208
ER -

References

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  1. Holditch’s theorem is somewhat deeper than Holditch thought in 1858, Normat 3 (1979), 89–100. (1979) Zbl0415.53003MR0548827
  2. 10.2307/2689793, Math. Mag. 54 (1981), 99–108. (1981) Zbl0468.51005MR0618595DOI10.2307/2689793
  3. 10.1016/S0094-114X(98)00028-7, Mech. Mach. Theory 34 (1999), 1–6. (1999) MR1738623DOI10.1016/S0094-114X(98)00028-7
  4. Geometrical theorem, Q.  J.  Pure Appl. Math. 2 (1858), 38–39. (1858) 
  5. Erweiterung des Satzes von Holditch für geschlossene Raumkurven, Abh. Braunschw. Wiss. Ges. 31 (1980), 129–135. (German) (1980) MR0608278
  6. Holditch-Sicheln, Arch. Math. 44 (1985), 373–378. (1985) Zbl0542.53008MR0788954
  7. Zum Satz von Holditch in der euklidischen Ebene, Elem. Math. 41 (1986), 1–6. (1986) Zbl0584.53005MR0880237
  8. 10.1007/BF01339077, Monatsh. Math. 80 (1975), 93–99. (1975) Zbl0318.53015MR0400071DOI10.1007/BF01339077
  9. Sätze vom Holditch-Typ für ebene Kurven, Elem. Math. 38 (1983), 39–49. (German) (1983) Zbl0468.53002MR0700282
  10. Calculus on Manifolds. A modern approach to classical theorems of advanced calculus, W. A. Benjamin, New York, 1965. (1965) Zbl0141.05403MR0209411
  11. 10.1023/B:CMAJ.0000042372.51882.a6, Czechoslovak Math. J. 54(129) (2004), 337–340. (2004) MR2059254DOI10.1023/B:CMAJ.0000042372.51882.a6
  12. Erweiterungen des Satzes von Holditch, Sitzungsber. Österr. Akad. Wiss. 184 (1975), 451–458. (German) (1975) MR0436011
  13. Ebene Kinematik, Verlag Oldenbourg, München, 1956. (German) (1956) MR0078790

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