Lin McMullin’s Theorem: an affine geometry assisted proof
I learned about this from Paysages Mathématique s, which in turn cites as source Theorem of the Day (March 15, 2025) by Robin Whitty. One can read online Lin McMullin’s description of how he found the theorem , a lovely mix of serendipity and computer aided calculation. The statement if as follows: consider y=f(x) in the plane, the graph of a quartic (degree 4) polynomial with two flexes p and q. Let L be the line through p and q, and let u and v be the other two intersections of L with the graph. Then the coordinates of u and v can be obtained from those of p and q via the formulas u= φp+(1-φ)q and v=(1-φ)p+ φq. McMullin found this by having a computer algebra system do the calculations for him. Of course the most amazing thing here is that he thought about this problem and imagined the result could be interesting! And it’s great he didn’t have to compute it all by hand (he may have been able to do so without error, I certainly wou...