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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, ....
FindDivisions[{xmin, xmax, {dx1, dx2, ...}}]
gives all numbers in the interval that are multiples of the dxi.
  • 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.
Find five divisions of the interval [0,1]:
Division end points may be outside the initial range:
Generate multiple levels of divisions:
Find divisions that are aligned to multiples of Pi:
Find divisions that are short in a given base:
Find five divisions of the interval [0,1]:
In[1]:=
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Out[1]=
 
Division end points may be outside the initial range:
In[1]:=
Click for copyable input
Out[1]=
 
Generate multiple levels of divisions:
In[1]:=
Click for copyable input
Out[1]=
 
Find divisions that are aligned to multiples of Pi:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Find divisions that are short in a given base:
In[1]:=
Click for copyable input
Out[1]//BaseForm=
In[2]:=
Click for copyable input
Out[2]//BaseForm=
In[3]:=
Click for copyable input
Out[3]//BaseForm=
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