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Letter from the Editor 3 Susan Jane Colley Neighbors of Knots in the Gordian Graph 4 Ryan Blair, Marion Campisi, Jesse Johnson, Scott A. Taylor, and Maggy Tomova The Falling Slinky 24 Robert J. Vanderbei Irreducibility Criteria for Reciprocal Polynomials and 37 Applications Antonio Cafure and Eda Cesaratto Seventy-Five Years of the Putnam Mathematical Competition 54 Joseph A. Gallian On a 2015 Putnam Problem Related to a Double Recursion 60 Nicolae Anghel NOTES Why Do All Triangles Form a Triangle? 70 Ian Stewart Chebyshev Polynomials and the Minimal Polynomial 74 of cos (2π/n) Yusuf Z. Gürtas ¸ Two-Sided, Unbiased Version of Hall's Marriage Theorem 79 Eli Shamir and Benny Sudakov Hausdorffization and Homotopy 81 Bart van Munster PROBLEMS AND SOLUTIONS 83 REVIEWS The Power of a Good Book 92 by Jason Rosenhouse MATHBITS 59, A Novel Way to Prove the Irrationality of 2; 73, A New Proof of the Finsler-Hadwiger Inequality An Official Publication of the Mathematical Association of America monthly THE AMERICAN MATHEMATICAL VO LU M E 1 24, N O. 1 JA N UA RY 20 1 7

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