Research ArticleOpen AccessGoogle Scholar indexed
On a Discrete Version of the Mohr-Mascheroni Theorem
Department of Mathematics, Computer Science, and Statistics, State University of New York, College at Oneonta, USA
Department of Mathematics, Computer Science, and Statistics, State University of New York, College at Oneonta, USA
- 1 Department of Mathematics, Computer Science, and Statistics, State University of New York, College at Oneonta, USA
- 2 Department of Mathematics, Computer Science, and Statistics, State University of New York, College at Oneonta, USA
Applied Mathematics·Volume 04 (2013)·Pages 11–13·Published 22 October 2013·DOI10.4236/am.2013.411A4002
Copy link · social · email
Abstract
We introduce a new geometric tool called n-compass and show that the famous theorem of Mascheroni and Mohr re mains valid if the traditional compass is replaced by the newly introduced tool.
KeywordsMohr-Mascheroni Theoremn-Compass
- L. Mascheroni, “Geometrie du Compas,” Monom, 1980.
- G. Mohr, “Euclides Danicus,” Copenhagen, 1928.
- N. Hungerbuhler, “A Short Elementary Proof of the Mohr-Mascheroni Theorem,” American Mathematical Monthly, Vol. 101, No. 8, 1994, pp. 784-797. http://dx.doi.org/10.2307/2974536
- A. Avron, “Theorems on Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 30, No. 1, 1987, pp. 28-35. http://dx.doi.org/10.1007/BF01223260
- A. Avron, “On Strict Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 38, No. 1-2, 1990, pp. 12-15. http://dx.doi.org/10.1007/BF01222890
- V. Pambuccian, “Axiomatizing Geometric Constructions,” Journal of Applied Logic, Vol. 6, No. 1, 2008, pp. 24-46. http://dx.doi.org/10.1016/j.jal.2007.02.001
- Z. Zhang, L. Yang and X. R. Hou, “What Can We Do with Only a Pair of Rusty Compasses?” Geometriae Dedicata, Vol. 38, 1991, pp. 137-150. http://dx.doi.org/10.1007/BF00181213
- V. J. Baston and F. A. Bostok, “On the Impossibility of Ruler-Only Constructions,” Proceedings of the American Mathematical Society, Vol. 110, No. 4, 1990, pp. 10171025. http://dx.doi.org/10.1090/S0002-9939-1990-1034882-3
- D. Fog, “Om Konstruktion Med Passeren Alene,” Mathematisk Tidsskrift A, 1935, pp. 16-24.
- V. S. Martynenko, “Mascheroni’s Theorem in Lobachevski Geometry,” Doklady Akademii Nauk Ukrainskoj SSR, Ser A, Vol. 1, 1982, pp. 22-27.