Editing Nomogram (section)

==Examples==

===Parallel-resistance/thin-lens===
[[Image:Nomogramparallelresistance.svg|right|200px|thumb|Parallel [[electrical resistance]] nomogram]]
The nomogram below performs the computation:

<math display=block>f(A,B)=\frac{1}{1/A+1/B}=\frac{AB}{A+B}</math>

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 <math>\sqrt{2}</math> 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 [[Series and parallel circuits#Parallel circuits|parallel-resistance formula]] in [[electronics]], and the [[Thin lens|thin-lens equation]] in [[optics]].

In the example, the red line demonstrates that parallel resistors of 56 and 42&nbsp;[[ohm]]s have a combined resistance of 24&nbsp;ohms. It also demonstrates that an object at a distance of 56&nbsp;cm from a [[lens (optics)|lens]] whose [[focal length]] is 24&nbsp;cm forms a [[real image]] at a distance of 42&nbsp;cm.
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===Chi-squared test computation===
[[Image:chisquarenomo3.png|right|200px|thumb|[[Chi-squared distribution]] nomogram]]
The nomogram below can be used to perform an approximate computation of some values needed when performing a familiar statistical test, [[Pearson's chi-squared test]]. This nomogram demonstrates the use of curved scales with unevenly spaced graduations.

The relevant expression is:

<math display="block">\frac{(OBS - EXP)^2}{EXP}</math>

The scale along the top is shared among five different ranges of observed values: A, B, C, D and E. The observed value is found in one of these ranges, and the tick mark used on that scale is found immediately above it. Then the curved scale used for the expected value is selected based on the range. For example, an observed value of 9 would use the tick mark above the 9 in range A, and curved scale A would be used for the expected value. An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value. This allows five different nomograms to be incorporated into a single diagram.

In this manner, the blue line demonstrates the computation of:

{{in5}} (9 &minus; 5)<sup>2</sup> / 5 = 3.2

and the red line demonstrates the computation of:

{{in5}} (81 &minus; 70)<sup>2</sup> / 70 = 1.7

In performing the test, [[Yates's correction for continuity]] is often applied, and simply involves subtracting 0.5 from the observed values. A nomogram for performing the test with Yates's correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart.
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===Food risk assessment===
[[Image:Risk Based Sampling Nomogram (3yr).png|right|200px|thumb|Food [[risk assessment]] nomogram]]
Although nomograms represent mathematical relationships, not all are mathematically derived.  The following one was developed graphically to achieve appropriate end results that could readily be defined by the product of their relationships in subjective units rather than numerically. The use of non-parallel axes enabled the non-linear relationships to be incorporated into the model.

The numbers in square boxes denote the axes requiring input after appropriate assessment.

The pair of nomograms at the top of the image determine the probability of occurrence and the availability, which are then incorporated into the bottom multistage nomogram.

Lines 8 and 10 are 'tie lines' or 'pivot lines' and are used for the transition between the stages of the compound nomogram.

The final pair of parallel logarithmic scales (12) are not nomograms as such, but reading-off scales to translate the risk score (11, remote to extremely high) into a sampling frequency to address safety aspects and other 'consumer protection' aspects respectively.  This stage requires political 'buy in' balancing cost against risk.  The example uses a three-year minimum frequency for each, though with the high risk end of the scales different for the two aspects, giving different frequencies for the two, but both subject to an overall minimum sampling of every food for all aspects at least once every three years.

This [[risk assessment]] nomogram was developed by the [[Public analyst|UK Public Analyst Service]] with funding from the [[Food Standards Agency|UK Food Standards Agency]] for use as a tool to guide the appropriate frequency of sampling and analysis of food for official food control purposes, intended to be used to assess all potential problems with all foods, although not yet adopted.
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===Other quick nomograms===
Using a ruler, one can readily read the missing term of the [[law of sines]] or the roots of the [[Quadratic equation|quadratic]] and [[Cubic function|cubic]] equation.<ref>{{cite journal|last1=Szalkai|first1=Istvan|last2=Balint|first2=Roland|title=Nomograms for the quadratic and cubic equations (in Hungarian)|journal=Haladvány Kiadvány|date=2017-12-28|volume=2017|url=http://math.bme.hu/~hujter/171228.pdf}}</ref>
<gallery>
File:SinT-nomogram-.gif|Nomogram for the law of sines
File:Nomogram-mf-egy-jav.gif|Nomogram for solving the quadratric x^2+px+q=0
File:Nomogram-BR-x3-1.png|Nomogram for solving the cubic x^3+px+q=0
</gallery>