Undirected value: Difference between revisions

Cmloegcmluin (talk | contribs)
Formula: hone connotations
Cmloegcmluin (talk | contribs)
better home for that identity
Line 76: Line 76:


To be clear, if the input is not already in ratio form, for example <math>\phi</math>, this formula requires it first to be placed over 1, like <math>\frac{\phi}{1}</math>.
To be clear, if the input is not already in ratio form, for example <math>\phi</math>, this formula requires it first to be placed over 1, like <math>\frac{\phi}{1}</math>.
=== Using a base ===
For the positives only (<math>x > 0</math>), we find an identity using logarithms and exponentiation:
<math>
\overline{\underline{x} = b^{|log_b(x)|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\
</math>


== Superunison, subunison, and unison numbers ==
== Superunison, subunison, and unison numbers ==
Line 185: Line 176:
|<math>\overline{\underline{x}}</math>
|<math>\overline{\underline{x}}</math>
|}
|}
The following identity shows the relationship between the undirected value and the absolute value, for positive real numbers.
<math>
\overline{\underline{x} = b^{|log_b(x)|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\
</math>


== Graphs ==
== Graphs ==