page_title: Nomogram
section_title: Parallel-resistance/thin-lens
hierarchical_section_title: Nomogram / Examples / Parallel-resistance/thin-lens
context_page_description: A nomogram, also called a nomograph, alignment chart, or abaque, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates.
  A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable. The virtual or drawn line created by the straightedge is called an index line or isopleth.
context_section_description: The nomogram below performs the computation
  This nomogram is interesting because it performs a useful nonlinear calculation using only straight-line, equally graduated scales. While the diagonal line has a scale  times larger than the axes scales, the numbers on it exactly match those directly below or to its left, and thus it can be easily created by drawing a straight line diagonally on a sheet of graph paper.
  A and B are entered on the horizontal and vertical scales, and the result is read from the diagonal scale.  Being proportional to the harmonic mean of A and B, this formula has several applications.  For example, it is the parallel-resistance formula in electronics, and the thin-lens equation in optics.
  In the example, the red line demonstrates that parallel resistors of 56 and 42 ohms have a combined resistance of 24 ohms. It also demonstrates that an object at a distance of 56 cm from a lens whose focal length is 24 cm forms a real image at a distance of 42 cm.
caption: Parallel electrical resistance nomogram