The Christmas Equation

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I posted the following in December 2021 on my first-year pure module's Piazza forum.

Hi everyone

I saw this a few years ago on QI, and found another version on the web at http://mathandmultimedia.com/2014/12/02/merry-christmas-equation/

If we are told that

\(\qquad\displaystyle y=\frac{\ln(\frac{x}m-sa)}{r^2}\)

multiplying by \(r^2\) gives

\(\qquad yr^2=\ln(\frac{x}m-sa)\,.\)

Then taking \(e\) to the power of both sides give

\(\qquad\displaystyle e^{yr^2}=\frac{x}m-sa\,,\)

and multiplying both sides by \(m\) gives

\(\qquad me^{yr^2}=x-msa\,,\)

which can be rewritten as

\(\qquad me^{rry}=x-mas\,.\)

(And a Happy New Year!)

Best wishes,

Dr Feinstein

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