Proving something fundamental (like the circumference of the earth!) or teaching dimensional analysis with animals, or graph theory, or simultaneous equations (which their teacher has told them to just guess at), or, well, y'all just have to read the thread. There's some incredibly fun stuff in here.
That a US state attempted to legislate a specific value for the number Pi and its possible consequences is also hilarious https://en.m.wikipedia.org/wiki/Indiana_pi_bill and gives itself to quite the discussion.
That a math theorem was proven by a US congressman, James Garfield, over a century ago https://en.m.wikipedia.org/wiki/Garfield's_proof_of_the_Pythagorean_theorem makes for another good discussion: it’s the Pythagoras theorem (and the proof is intuitive and easy to explain by drawing and measuring areas of triangles), and sets a baseline of expectations for the intellectual capabilities of anyone running for office … or it should.
@albertcardona so much good in here. And these are quick kids -- I think the multiple layers of ridiculousness in the attempted legislation of pi would not be lost on them!
@DrTCombs My wife says, "I would do the derivation of e. There's a really cute derivation of e... actually multiple cute derivations of e.
Maybe also derive the pythagorean theorem? There's a geometric proof. If they haven't seen pi by then, they should be introduced to it. They wouldn't understand it fully, but I would show them a youtube video of the harmonics of the riemann zeta function. It's so amazing to see. OOH nonlinear dynamics the butterfly oscillator!"
@DrTCombs Eulerian circuits and the 7 bridges of Konigsberg! It's a simple enough problem to describe to smart kids of that age, and demonstrates some fundamental graph theory, which is an entirely different branch of math than most kids ever get exposed to.
@DrTCombs multiplying and dividing silly things like fractions of cats and dogs might be fun, story problems, a taste of algebra, and is analogous to multiplying units, which helps keep your conversions right since cat/cat = 1... Like 3/4 liters water balloon per dog * 2 dogs per 4 cats... IDK that example needs work
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