请输入您要查询的字词:

 

单词 LazyCaterersSequence
释义

lazy caterer’s sequence


Given a pancake (or a circle), how can one cut n pieces (not necessarily of the same size) with the minimum number of cuts? For example, to cut a pancake into four pieces, four cuts could be made, each starting at the center and going to the edge. But it would be much simpler to make just two cuts to cut it into four pieces.

The maximum number of pieces that can be created with a given number of cuts n is given by the formula

n2+n+22

which gives the lazy caterer’s sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, … (listed in A000124 of Sloane’s OEIS).

The numbers of this sequence are also called central polygonal numbers, and have applications in various other mathematical problems. Each of these numbers is 1 plus a triangular numberMathworldPlanetmath.

Shel Kaphan, in a remark to the OEIS writes that ”when constructing a zonohedron, one zone at a time, out of (up to) 3-D non-intersecting parallelepipedsMathworldPlanetmath, the nth element of this sequence is the number of edges in the nth zone added with the nth layer of parallelepipeds.”

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/5 2:19:21