Finding polynomials from a set of coordinates

[Dieter]

(03-12-2017 08:27 PM)Csaba Tizedes Wrote:  1.) Why do not teach him how he can decide which polynomial degree is sufficient to fit?

Sure – why not? Go ahead! ;-)

(03-12-2017 08:27 PM)Csaba Tizedes Wrote:  2.) What about your 6th degree model first derivative in t=0 and t=24? As I guess these values aren't same - so that is not a good solution.

Yes, f'(0) and f'(24) being equal would be nicer.
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, although it's not what the OP asked for.

Dieter