FindDivisions

FindDivisions[{xmin,xmax},n]

finds a list of about n "nice" numbers that divide the interval around xmin to xmax into equally spaced parts.

FindDivisions[{xmin,xmax,dx},n]

makes the parts always have lengths that are integer multiples of dx.

FindDivisions[{xmin,xmax},{n1,n2,…}]

finds successive subdivisions into about n1, n2, … parts.

FindDivisions[{xmin,xmax,{dx1,dx2,…}},{n1,n2,…}]

uses spacings that are forced to be multiples of dx1, dx2, ….

Details and Options

  • FindDivisions[{xmin,xmax},n] searches for numbers that are shortest in their decimal representation.
  • FindDivisions[{xmin,xmax},n,k] searches for numbers that are shortest in their base k representation.
  • The first and last numbers may be slightly outside the range xmin to xmax.
  • The dxi can be exact numbers such as Pi/2 specified in symbolic form.
  • FindDivisions[{xmin,xmax},{n1,n2,…}] yields a list of lists, in which later lists omit elements that occur in earlier lists.
  • For some choices of dxi, some of the lists generated may be empty.

Examples

Basic Examples  (5)

Find five divisions of the interval [0,1]:

Division endpoints may be outside the initial range:

Generate multiple levels of divisions:

Find divisions that are aligned to multiples of :

Find divisions that are short in a given base:

Wolfram Research (2008), FindDivisions, Wolfram Language function, https://reference.wolfram.com/language/ref/FindDivisions.html.

Text

Wolfram Research (2008), FindDivisions, Wolfram Language function, https://reference.wolfram.com/language/ref/FindDivisions.html.

CMS

Wolfram Language. 2008. "FindDivisions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindDivisions.html.

APA

Wolfram Language. (2008). FindDivisions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindDivisions.html

BibTeX

@misc{reference.wolfram_2024_finddivisions, author="Wolfram Research", title="{FindDivisions}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FindDivisions.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_finddivisions, organization={Wolfram Research}, title={FindDivisions}, year={2008}, url={https://reference.wolfram.com/language/ref/FindDivisions.html}, note=[Accessed: 22-December-2024 ]}