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math.CA2003
Ratio vectors of fourth degree polynomials
Alan Horwitz
Let p(x) be a polynomial of degree 4 with four distinct real roots r1<r2<r3<r4. Let x1<x2<x3 be the critical points of p, and define the ratios s_{k}=((x_{k}-r_{k})/(r_{k+1}-r_{k})…
math.CA2003★ 1 cited
The locus of centers of ellipses inscribed in quadrilaterals
Alan Horwitz
Let R be a four-sided convex polygon in the xy plane and let M1 and M2 be the midpoints of the diagonals of R. It is well-known that if E is an ellipse inscribed in R, then the cen…