|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Evolutes and involutes of frontals in the Euclidean plane
| Title: | Evolutes and involutes of frontals in the Euclidean plane |
| Authors: | Fukunaga, Tomonori Browse this author | | Takahashi, Masatomo Browse this author |
| Keywords: | evolute | | involute | | frontal | | Legendre curve | | inflection point |
| Issue Date: | 31-Mar-2014 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1052 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | We have already defined the evolutes and the involutes of fronts without inflection points. For regular curves or fronts, we can not define the evolutes at inflection points. On the other hand, the involutes can be defined at inflection points. In this case, the involute is not a front but a frontal at inflection points. We define evolutes of frontals under conditions. The definition is a generalisation of both evolutes of regular curves and of fronts. By using relationship between evolutes and involutes of frontals, we give an existence condition of the evolute with inflection points. We also give properties of evolutes and involutes of frontals. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69856 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
