I always liked nomograms! Most of them are pieces or art!
But what is a nomogram (or nomograph)?
A nomogram (from Greek νόμος nomos, "law" and γραμμή grammē, "line"), also called a nomograph is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.
Nomograms have been used in an extensive array of applications like Statistics, Aeronautics, Astronomical calculations, Engineering work of all kind.
Nomograms were fast, compact, accurate, quick and easy-to-use calculators.
Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines!
About this project...
I ll show you how to create a nomogram that can help you calculate the ph of a dilution when you mix two dilutions with different ph
For this project you ll need:
A4 millimeter paper (or bigger. it depends on how big you want it)
pen and pencil
rule and triangle
elastic curve for drawing
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Step 1: Orient Your Nomogram
take the A4 graph paper, put it horizontally and then draw a horizontal line 4 cm above the marfin. then make a vertical line exactly in the middle (14 cm from the margins).
Step 2: Put the Scales
the horizontal axle is in metric scale.
put the numbers firstly on the horizontal scale as shown in the photo. the scale is metric so you ll put the numbers (14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
DONT PUT ZERO!
the vertical axle is in logarithmic scale. you ll put the numbers in the vertical axle (the numbers that are written in bold)
log1=0 x 10= 0, log2=0.3 x 10= 3, log3=0.48 x 10= 4.8, log4=0.6 x 10= 6, log5=0,7 x 10= 7, log6=0,78 x 10= 7.8
log7=0,85 x 10= 8.5 , log8=0.9 x 10= 9, log9=0.95 x 10= 9.5 , log10=1 x 10= 10 , log11=1.04 x 10= 10.4
log12=1.08 x 10= 10.8 , log13=1.11 x 10= 11.1 , log14=1.15 x 10= 11.5
Step 3: Marking the Graph
this step is very easy. you just mark the couples of the coordinates (1,1) , (2,2) ....( 14,14) and put numbers next to the marking point
Step 4: Make the Curve
use the elastic curve (or your hand) and make two curves that pass above the marks.
Step 5: It Is Ready!
the curve on the left side is for the ph of the first dilution and the curve on the right is for the ph of the second dilution.
make a line that connects two points. the point that crosses the vertical axle shows the ph of the final dilution!
Step 6: Play With It!
just play with it. calculate ph by just making lines! you ll discover a lot of things about logarithms and mixxing!
as i mention, this nomogram was for equal volumes of dilutions. you can make more curves on each side if you want to count the ph of dilution with different ratio of volumes. on my nomogram i added one more curve (just divide (or multiply) the horizontal scale).
note: Nomogram's accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. the precision of this nomogram is not very good when you want to find ph around 1.
Step 7: Isnt It ART?
isnt is ART?
This is an entry in the
Made with Math Contest