“Euclid's orchard”的意思、由来-开放百科全书

词条

Euclid's orchard

释义

See also
References
External links

In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice.^[1] More formally, Euclid's orchard is the set of line segments from {{nowrap|(i, j, 0)}} to {{nowrap|(i, j, 1)}}, where i and j are positive integers.

The trees visible from the origin are those at lattice points {{nowrap|(m, n, 0)}}, where m and n are coprime, i.e., where the fraction {{sfrac|m|n}} is in reduced form. The name Euclid's orchard is derived from the Euclidean algorithm.

If the orchard is projected relative to the origin onto the plane {{nowrap|1=x + y = 1}} (or, equivalently, drawn in perspective from a viewpoint at the origin) the tops of the trees form a graph of Thomae's function. The point {{nowrap|(m, n, 1)}} projects to

References

1. ^{{MathWorld|urlname=EuclidsOrchard|title=Euclid's Orchard}}

External links

Euclid's Orchard, Grade 9-11 activities and problem sheet, Texas Instruments Inc.
[https://projecteuler.net/problem=351 Project Euler related problem]

2 : Greek_mathematics|Lattice points

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

See also

References

External links