Finding polynomials from a set of coordinates

[Csaba Tizedes]

(03-12-2017 11:31 PM)Dieter Wrote:  Of course calculating a periodoc function is possible as well. Here is a possible result with a period of 24 hours:

temperature ~ 12 – 13/3 cos(r*t) + 1/3 cos(3r*t) – 8/sqrt(3) sin(r*t) – 1/sqrt(3) sin(2r*t)

where r = 2pi/24 = pi/12

This may be a better solution

And the second part of my answer about the periodic function:

If I'm sitting in the middle of nowhere and I want to fit a periodic function, I will use the simplest solution:

1.) This is about a data of one day: the period is 24 hours
2.) The min and max values are exactly at t=4h and at t=16h
3.) Therefore the inflection is between them at t=10h
4.) The range of data between the max and min values of temperature, therefore we can calculate the amplitude of periodic function and the mean value for the shift of the function
5.) If I want to more exact value for the shift on the temperature axis, I can calculate the average of the measured temperatures - this requires little more keypress, no problem, I like it
6.) Just for fun, draw a little diagram and calculate the temperature differences and calculate RMS

Everything fits in this half letter paper:

   

And I used only one piece of paper, one of my favourite durable pencil and my most durable HP15C.

   

This IS the engineering problem solving, not the sooo looong equuuuaaatioooons with looots of coefficients.

Csaba

PS.: I have no problem with you, I hope you're feel it, I'm just this kind of men.