Dimensional analysis

This series of articles takes a detailed look at dimensional analysis, an important and surprisingly subtle branch of mathematical physics. We can determine a lot about a physical system by examining the units of measurement that we use to describe it, often without needing to perform difficult calculations.

Starting from an intuitive description of the project of dimensional analysis, we build to a derivation of its central theorem: the Buckingham Pi theorem. We then show how one can automate the computation of the central quantities in a dimensional analysis problem. Along the way, we look at a number of examples and historical episodes.

  1. Introduction to dimensional analysis


  2. Nondimensional numbers and the Buckingham Pi theorem


  3. Linear algebra and the Buckingham Pi theorem

    \begin{equation*} p = n-k \end{equation*}


  4. Automated dimensional analysis


  5. Ultriviolet catastrophe and the beginning of quantum mechanics