Envelopes of straight line families in the plane
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910436419436544 |
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| author | Nishimura, Takashi |
| author_facet | Nishimura, Takashi |
| contents | There is a widespread method to represent the envelope when a given hyperplane family creates an envelope. However, one sometimes encounters cases when the widespread method fails to represent the desired envelope precisely, and is confused. At the same time, one wants to find a correct method to draw the envelope precisely.
In this article, focused on straight line families in the plane, an easy to understand explanation is given on the recently discovered correct method to represent the envelope precisely. Moreover, it is explained when and why the widespread method fails to represent the precise shape of envelope as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Envelopes of straight line families in the plane Nishimura, Takashi Differential Geometry 57R45, 58C25 There is a widespread method to represent the envelope when a given hyperplane family creates an envelope. However, one sometimes encounters cases when the widespread method fails to represent the desired envelope precisely, and is confused. At the same time, one wants to find a correct method to draw the envelope precisely. In this article, focused on straight line families in the plane, an easy to understand explanation is given on the recently discovered correct method to represent the envelope precisely. Moreover, it is explained when and why the widespread method fails to represent the precise shape of envelope as well. |
| title | Envelopes of straight line families in the plane |
| topic | Differential Geometry 57R45, 58C25 |
| url | https://arxiv.org/abs/2307.07232 |