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Hokkaido University Preprint Series in Mathematics >
Evolutes of fronts in the Euclidean plane
| Title: | Evolutes of fronts in the Euclidean plane |
| Authors: | Fukunaga, Tomonori Browse this author | | Takahashi, Masatomo Browse this author |
| Keywords: | evolute | | parallel curve | | front | | Legendre immersion |
| Issue Date: | 17-Dec-2012 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1026 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | The evolute of a regular curve in the Euclidean plane is given by not only the caustics of the regular curve, envelope of normal lines of the regular curve, but also the locus of singular loci of parallel curves. In general, the evolute of a regular curve have singularities, since such a point is corresponding to a vertex of the regular curve and there are at least four vertices for simple closed curves. If we repeated an evolute, we cannot define the evolute at a singular point. In this paper, we define an evolute of a front and give properties of such evolute by using a moving frame of a front and the curvature of the Legendre immersion. As applications, repeated evolutes can be well-defined and these are useful to recognize the shape of curves. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69831 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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