A guess to start

The formula, but not the explanation

Planck's first step was to try to set up an empirical formula which reduces to Wien's at short wavelengths and to Rayleigh-Jeans' at long wavelengths. Mathematically this is not too difficult. Planck achieved such a formula simply by putting an additional term into the denominator of Wien's law. The only justification for this mathematical trick was that it works!

Planck's merger of two curves mathematically

Wien's spectral distribution law

Rayleigh-Jeans law

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Planck's 'lucky guess'

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