Nomogram
A nomogram ( Greek νόμος nomos , 'law' and γραμμή grammē , 'line'), German network table , is a diagram on which the values of a mathematical function can be read approximately. Nomography (teaching how to create nomograms) was founded in 1850 by Léon Lalanne and Maurice d'Ocagne . The accuracy with which the function values are read depends on the accuracy with which the markings can be read.
A nomogram usually contains scales on which known values are plotted and a scale on which the result can be read. If the nomogram is a function of two variables, then there are two scales on which the values of the variables can be found and one scale that contains the values / results sought. If you connect the two points on the scales where the variable values are located by a straight line, this intersects the result scale. The point of intersection with the result scale indicates the function value.
The scale lines are rarely straight. Complicated functions can often be better indicated by using curvilinear scale curves.
Example nomograms
Example 1: Simple nomogram for calculating . The calculation is shown as an example (red line) . (The line connects 42 on the x-axis and 56 on the y-axis . The result 24 can be read off as the intersection with the diagonal.) This can e.g. B. can be used to calculate the electrical resistance when connected in parallel (or the capacitance when connected in series ). | Example 2: Smith chart shows how the complex impedance varies with the length of a transmission line |
Further examples
literature
- Maurice d'Ocagne: Traité de Nomographie. Theorie des abacques, applications pratiques . Gauthier-Villars, Paris 1899.
- Maurice d'Ocagne: Sur la résolution nomographique de l'équation du septième degré . In: Comptes rendus mathematique . 131: 522-524 (1900), ISSN 1631-073X .
Web links
- A nomogram of an oscillating circuit
- Hilbert's 13th problem
- PyNomo - open source software for creating nomograms