HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

Involutes of fronts in the Euclidean plane

Files in This Item:
pre1045.pdf199.28 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/84189

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
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

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University