TY - JOUR
T1 - The equal tangents property
AU - Jerónimo-Castro, Jesús
AU - Ruiz-Hernández, Gabriel
AU - Tabachnikov, Sergei
N1 - Publisher Copyright:
© de Gruyter 2014.
PY - 2014/7/1
Y1 - 2014/7/1
N2 - Let M be a C2-smooth strictly convex closed surface in ℝ3 and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths. In this note we prove that if H is either a closed surface containing M or a plane, then M is a Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different.
AB - Let M be a C2-smooth strictly convex closed surface in ℝ3 and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths. In this note we prove that if H is either a closed surface containing M or a plane, then M is a Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different.
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U2 - 10.1515/advgeom-2013-0011
DO - 10.1515/advgeom-2013-0011
M3 - Article
AN - SCOPUS:84925373760
SN - 1615-715X
VL - 14
SP - 447
EP - 453
JO - Advances in Geometry
JF - Advances in Geometry
IS - 3
ER -