Convex curves of bounded type
Let C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke's Rolling Theor...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000680 |
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doaj-dc5341e90aa64d6da1359292cb2abf862020-11-24T23:04:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018462563310.1155/S0161171285000680Convex curves of bounded typeA. W. Goodman0Mathematics Department, University of South Florida, Tampa 33620, Florida, USALet C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke's Rolling Theorem. We prove one new theorem and suggest a number of open problems.http://dx.doi.org/10.1155/S0161171285000680convex curvebounded typeperimeter centroidBlaschke's rolling theoremparallel curvemass distribution on a curve. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. W. Goodman |
| spellingShingle |
A. W. Goodman Convex curves of bounded type International Journal of Mathematics and Mathematical Sciences convex curve bounded type perimeter centroid Blaschke's rolling theorem parallel curve mass distribution on a curve. |
| author_facet |
A. W. Goodman |
| author_sort |
A. W. Goodman |
| title |
Convex curves of bounded type |
| title_short |
Convex curves of bounded type |
| title_full |
Convex curves of bounded type |
| title_fullStr |
Convex curves of bounded type |
| title_full_unstemmed |
Convex curves of bounded type |
| title_sort |
convex curves of bounded type |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1985-01-01 |
| description |
Let C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke's Rolling Theorem. We prove one new theorem and suggest a number of open problems. |
| topic |
convex curve bounded type perimeter centroid Blaschke's rolling theorem parallel curve mass distribution on a curve. |
| url |
http://dx.doi.org/10.1155/S0161171285000680 |
| work_keys_str_mv |
AT awgoodman convexcurvesofboundedtype |
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1725628573770842112 |