請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61902完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農(Ai-Nung Wang) | |
| dc.contributor.author | Chih-Ju Huang | en |
| dc.contributor.author | 黃志儒 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:17:57Z | - |
| dc.date.available | 2013-07-31 | |
| dc.date.copyright | 2013-07-31 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-27 | |
| dc.identifier.citation | [1] R. L. Foote, M. Levi, S. Tabachnikov, Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture, arXiv:1207.0834v1.
[2] R. Foote, Geometry of the Prytz Planimeter, Reports Math. Physics 42 (1998), 249–271. [3] F. W. Hill, The Hatchet Planimeter, Philosophical magazine, S. 5, Vol. 38, No 232, Sept., 1894, 265–269; Proc. of the Physical Society 13, 229–234 (same paper appears twice). [4] L.Santalo, Integral Geometry and Geometric Probability. Cambridge University Press, Cambridge, 2004. [5] H. Hopf, Differential geometry in the large. Lecture Notes in Mathematics, 1000. Springer-Verlag, Berlin, 1983. [6] S. Howe, M. Pancia, V. Zakharevich, Isoperimetric Inequality for wave fronts and a generalization of Menzin’s Conjecture for bicycle monodromy on surfaces of constant curvature, Adv. Geom. 11 (2011), 273-292. [7] A. Beardon. The geometry of discrete groups. Springer-Verlag, 1983. [8] C.Care, Illustrating the history of the planimeter, http://empublic.dcs.warwick.ac.uk/projects/planimeterCare2004/Docs/report.pdf. [9] A. L. Menzin, The tractigraph, an improved form of hatchet planimeter, Engineering News, 56, No. 6, 1906, 131–132. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61902 | - |
| dc.description.abstract | 先討論自行車運動時前後輪應有的關係，以及測面儀的應用。這兩者的運動模式都依循著「自行車制約」，但它們運動的結果卻有著截然不同的現象。Menzin為造成不同現象的原因提出了一個猜想。最後來討論這個猜想，證明在前輪走凸封閉曲線的狀況下的個猜想是對的。 | zh_TW |
| dc.description.abstract | First we compare how a bicycle behaves with how a Prytz planimeter works. A planimeter is an instrument that used to measure the area bounded by a closed curve. There are many type of planimeters, while the Prytz planimeter works the same as a bicycle, but has a totally different phenomenon. Menzin characterised these phenomenon. We also prove the Menzin's Conjecture under a special case that the front wheel moves in a convex closed curve. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:17:57Z (GMT). No. of bitstreams: 1 ntu-102-R99221004-1.pdf: 1120240 bytes, checksum: 6008604958743e1c96f5b42f1f548de8 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 口試委員會審定書 . . . . . . . . . . . . . . . . . . . . . i
Acknowlegement . . . . . . . . . . . . . . . . . . . . ii Abstract (in Chinese) . . . . . . . . . . . . . . . . iii Abstract (in English) . . . . . . . . . . . . . . . . iv Contents . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . vi 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 2 Bicycle monodromy . . . . . . . . . . . . . . . . . . 6 2.1 The Area Between the Front and Rear Trajectory . . 6 2.2 Some Differential Equations . . . . . . . . . . 12 3 Menzin’s Conjecture . . . . . . . . . . . . . . . . 14 3.1 Envelope of a family of lines . . . . . . . . . 14 3.2 Proof of Menzin’s Conjecture . . . . . . . . . . 16 Bibliography . . . . . . . . . . . . . . . . . . . . . 21 | |
| dc.language.iso | en | |
| dc.subject | 自行車 | zh_TW |
| dc.subject | 凸曲線 | zh_TW |
| dc.subject | 腳踏車 | zh_TW |
| dc.subject | Menzin | zh_TW |
| dc.subject | 測面器 | zh_TW |
| dc.subject | 測面儀 | zh_TW |
| dc.subject | 固定點 | zh_TW |
| dc.subject | convex | en |
| dc.subject | fixed point | en |
| dc.subject | planimeter | en |
| dc.subject | Menzin | en |
| dc.subject | bicycle | en |
| dc.title | 自行車的制約與Menzin猜想 | zh_TW |
| dc.title | Bicycle Constraint and Menzin’s Conjecture | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡宜洵(I-Hsun Tsai),莊正良(Chen-Lian Chuang) | |
| dc.subject.keyword | 自行車,腳踏車,Menzin,測面器,測面儀,固定點,凸曲線, | zh_TW |
| dc.subject.keyword | bicycle,Menzin,planimeter,fixed point,convex, | en |
| dc.relation.page | 21 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-29 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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