Involutes of fronts in the Euclidean plane

Fukunaga, Tomonori; Takahashi, Masatomo

Hokkaido University Preprint Series in Mathematics, 2013, 1045, 1-20

Permalink : https://doi.org/10.14943/84189

このアイテムのアクセス数:901件（2026-08-25 16:54 集計）

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アクセス権	open access
DOI	https://doi.org/10.14943/84189
URI	https://hdl.handle.net/2115/69849
タイトル	Involutes of fronts in the Euclidean plane
著者	著者名 Fukunaga, Tomonori
著者	著者名 Takahashi, Masatomo
言語	英語
キーワード	involute
	evolute
	front
	Legendre immersion
	inflection point
発行日	2013-11-21
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1045
ページ	1-20
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record