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Characterizations of the sphere by means of visual cones: an alternative proof of Matsuura's theorem Amaya, Efren Morales
Description
In this work we prove that if there exists a point $p\in \mathbb{R}^n$ and a smooth convex body $M$ in $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, such that $M$ looks centrally symmetric, and $p$ appears as the centre, from each point of $\mathbb{S}^{n-1}$, then $M$ is an sphere. Using this result we derived, straightaway, a well known characterization of the sphere due to S. Matsuura
Item Metadata
Title |
Characterizations of the sphere by means of visual cones: an alternative proof of Matsuura's theorem
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-10-10T11:57
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Description |
In this work we prove that if there exists a point $p\in \mathbb{R}^n$ and a smooth convex body $M$ in $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, such that $M$ looks centrally symmetric, and $p$ appears as the centre, from each point of $\mathbb{S}^{n-1}$, then $M$ is an sphere. Using this result we derived, straightaway, a well known characterization of the sphere due to S. Matsuura
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Extent |
11.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universidad Autónoma de Guerrero
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Series | |
Date Available |
2020-04-08
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0389769
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International