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Hokkaido University Preprint Series in Mathematics >
Involutes of fronts in the Euclidean plane
| Title: | Involutes of fronts in the Euclidean plane |
| Authors: | Fukunaga, Tomonori Browse this author | | Takahashi, Masatomo Browse this author |
| Keywords: | involute | | evolute | | front | | Legendre immersion | | inflection point |
| Issue Date: | 21-Nov-2013 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1045 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | The notions of involutes (also known as evolvents) and evolutes were studied by C. Huygens. For a regular plane curve, an involute of it is the trajectory described by the end of stretched string unwinding from a point of the curve. Even if a regular curve, the involute of the curve have singularities. By using a moving frame of the front and the curvature of the Legendre immersion in the unit tangent bundle, we define an involute of the front in the Euclidean plane and discuss properties of them. We also consider about relationship between evolutes and involutes of fronts without inflection points. As a result, we observe that the evolutes and the involutes of fronts without inflection points are corresponding to the differential and the integral in classical calculus. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69849 |
| 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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