How do I quickly and easily interpolate a point on a chart without given data?

  • Thread starter Thread starter usfz28
  • Start date Start date
  • Tags Tags
    Interpolation
AI Thread Summary
To interpolate a point on a chart without given data, represent the two boundary points as a line on a Cartesian graph. Use basic algebra to derive the equation of the line, which allows for finding the missing coordinate. While some interpolation methods may not always yield accurate results, understanding the underlying principles can help. Resources like Wikipedia and specific engineering documents can provide additional guidance. Mastering these techniques is crucial for efficiently handling data in thermodynamics tests.
usfz28
Messages
19
Reaction score
0
I completely forgot how to do this. I have a thermo test coming up and i will be interpolating a lot of data. What is the fastes/easiest way to interpolate a point on a chart not given?
 
Physics news on Phys.org
yea already looked at that...The first eq. on this site is much easier but someitmes it does not work http://engineering.union.edu/~brunob/mer026/Thermo%20intro%20interpolation.doc
 
Last edited by a moderator:
usfz28 on linear interpolation said:
someitmes it does not work
when is that?
 
Think of how the data would appear on a cartesian graph. Represent the two boundary points as a line. You only need simple elementary algebra about equations for a line to find the missing coordinate.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
Back
Top