Bibliographic Details
| Title: |
On Lines and Joints. |
| Authors: |
Kaplan, Haim1 haimk@post.tau.ac.il, Sharir, Micha michas@post.tau.ac.il, Shustin, Eugenii2 shustin@post.tau.ac.il |
| Source: |
Discrete & Computational Geometry. Dec2010, Vol. 44 Issue 4, p838-843. 6p. |
| Subjects: |
Line geometry, Algebraic curves, Mathematical proofs, Number theory, Boundary value problems, Dimensional analysis, Mathematical analysis |
| Abstract: |
Let L be a set of n lines in ℝ, for d≥3. A joint of L is a point incident to at least d lines of L, not all in a common hyperplane. Using a very simple algebraic proof technique, we show that the maximum possible number of joints of L is Θ( n). For d=3, this is a considerable simplification of the original algebraic proof of Guth and Katz (Algebraic methods in discrete analogs of the Kakeya problem, 4 December , ), and of the follow-up simpler proof of Elekes et al. (On lines, joints, and incidences in three dimensions. Manuscript, 11 May , ). Some extensions, e.g., to the case of joints of algebraic curves, are also presented. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
