The study of cyclic equilateral polygon of order n partitioned area anda stroke problem
| Autor: | I-Hsin Liao, 廖宜新 |
|---|---|
| Rok vydání: | 2006 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 94 This study was to explore a stroke problem of cyclic equilateral polygon of order n partitioned area, and the number of cyclic equilateral polygon of order n partitioned area. The researcher used Eulerian theorem to explore one stroke problem, and then used Turbo C language to write equation and to calculate the points of intersection of two arbitrary chords. Finally, the researcher used Eulerian formula to calculate the number of the partitioned area. The main findings of the study were stated as two aspects： 1.A stroke problem of cyclic equilateral polygon of order n partitioned area The researcher used Eulerian theorem found：If cyclic odd number equilateral polygon, then the chords of the connected vertexes partitioned area could use one stroke to complete； If cyclic even number equilateral polygon, then the chords of the connected vertexes partitioned area could not use one stroke to complete. 2.The number of cyclic equilateral polygon of order n partitioned area （1）n is odd number This study found n＝3~35, the partitioned area is one of the maximum area graph, when vertexes of cyclic equilateral polygon of order n connected partitioned area graph is cyclic polygon of order n. （2）n is even number This study found n＝4~36, the researcher extrapolated, the partitioned area is one of the minimum area graph, when vertexes of cyclic even number equilateral polygon of order n connected partitioned area graph is cyclic even number polygon of order n. Key words：cyclic, equilateral polygon of order n, partition, one stroke, Eulerian theorem, Eulerian formula |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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