منابع مشابه
The Law of Tangents
Most geometry and pre-calculus books have entire units devoted to learning about two of the most important formulas in mathematics: the law of sines and the law of cosines. Both of these are very useful and very powerful tools, as they can be used to find unknown angles and sides of triangles. Yet, these books rarely devote anything to another formula that is equally powerful and useful: the la...
متن کاملThe equal tangents property
Let M be a C-smooth strictly convex closed surface in R 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 an Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different. 1 In the Euclidean...
متن کاملThe (Un)equal Tangents Problem
Given a point A outside of a closed strictly convex plane curve γ, there are two tangent segments from A to γ, the left and the right ones, looking from point A. Problem: Does there exist a curve γ such that one can walk around it so that, at all moments, the right tangent segment is smaller than the left one? In other words, does there exist a pair of simple closed curves, γ and Γ, the former ...
متن کاملTangents of plurisubharmonic functions
Tangents of plurisubharmonic functions Local properties of plurisubharmonic functions are studied by means of the notion of tangent which describes the behavior of the function near a given point. We show that there are plurisubharmonic functions with several tangents, disproving a conjecture of Reese Harvey.
متن کاملTangents to Subsolutions
There is an interesting potential theory associated to each degenerate elliptic, fully nonlinear equation f(Du) = 0. These include all the potential theories attached to calibrated geometries. This paper begins the study of tangents to the subsolutions in these theories, a topic inspired by the results of Kiselman in the classical plurisubharmonic case. Fundamental to this study is a new invari...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.09.012