# 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]:

 In:= Out= Division endpoints may be outside the initial range:

 In:= Out= Generate multiple levels of divisions:

 In:= Out= Find divisions that are aligned to multiples of :

 In:= Out= In:= Out= Find divisions that are short in a given base:

 In:= Out//BaseForm= In:= Out//BaseForm= In:= Out//BaseForm= Introduced in 2008
(7.0)