BUILT-IN MATHEMATICA SYMBOL

# FindDivisions

FindDivisions[{xmin, xmax}, n]
finds a list of about n "nice" numbers that divide the interval around to 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 , , ... parts.

FindDivisions[{xmin, xmax, {dx1, dx2, ...}}, {n1, n2, ...}]
uses spacings that are forced to be multiples of , , ....

FindDivisions[{xmin, xmax, {dx1, dx2, ...}}]
gives all numbers in the interval that are multiples of the .

## Details and OptionsDetails 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 to .
• The 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 , some of the lists generated may be empty.

## ExamplesExamplesopen allclose all

### Basic Examples (5)Basic Examples (5)

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

 Out[1]=

Division end points may be outside the initial range:

 Out[1]=

Generate multiple levels of divisions:

 Out[1]=

Find divisions that are aligned to multiples of :

 Out[1]=
 Out[2]=

Find divisions that are short in a given base:

 Out[1]//BaseForm=
 Out[2]//BaseForm=
 Out[3]//BaseForm=

## See AlsoSee Also

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