American Mathematical Monthly

Article	Citations
A Dynamic Kelly Criterion for Games with a Maximum Payout	15
Problems and Solutions	7
Reviews	6
100 Years Ago This Month in The American Mathematical Monthly	5
100 Years Ago This Month in The American Mathematical Monthly	5
The Altitudes of a Triangle	5
The Mathematical Community Working To Create Better (And Free!) Textbooks	5
A Generalization of Schatunowsky’s Theorem	5
My Friend Abe Shenitzer	5
Problems and Solutions	4
A Jeep Crossing a Desert of Unknown Width	4
Polynomial Approximations to Continuous Functions	4
Moon in a Puddle and the Four-Vertex Theorem	4
Pentagram Configurations for Pentagons and Hexagons	4
Six Houses and Three Utilities on A Coffee Mug	4
Gaussian Binomial Coefficients in Group Theory, Field Theory, and Topology	4
On Erdős’s Proof of the Existence of Cages	3
Lucky Cars: Expected Values and Generating Functions	3
Problems and Solutions	3
On Liouville’s Theorem for Conformal Maps	3
Problems and Solutions	3
A Number System with Base	3
100 Years Ago This Month in The American Mathematical Monthly	3
A Non-Terminating Game of Beggar-My-Neighbor	2
Galileo’s Swiftest Descent Problem Revisited: Complete Analytic Solution	2

The Paul R. Halmos–Lester R. Ford Awards for 2024	2
Optimizing for the Rupert Property	2
Alice and Bob on ????: Reversal, Coupling, Renewal	2
Honsberger-Type Identities via Busche-Ramanujan Identity	2
Averages in Projectile Motion with Linear and Quadratic Drag	2
Moments in the Exact Summation of the Curious Series of Kempner Type	2
A Tale of Two Cyclicities: Counting in Finite Cyclic Groups and Finite Fields	2
Reviews	2
An Elementary Solution of the Basel Problem	2
Romance of Mathematics	2
How to Prove it with Lean	2
On a Geometry Problem in Plato’s Meno	2
On the Chromatic Number of the Plane with Two Forbidden Distances	2
A Combinatorial Proof of the Existence of Dense Subsets in ℝ without the “Steinhaus” like Property	2
Reviews	2
In Search of Comrade Agronomof: Some Tribonacci History	2
The Abel–Ruffini Theorem: Complex but Not Complicated	2
Tiling with Monotone Polyominos	2
A New Polygonal Number Theorem	2
A New Theorem for Mixed Partial Derivatives	2
Launching a Data Analytics Major: How Collaboration and Agility Built a Successful Program	1
A Thābit-like Extension of the Pythagorean Theorem	1
100 Years Ago This Month in The American Mathematical Monthly	1
Stirling’s Formula Without Calculus	1
Monthly Referees for 2022	1
An Inequality of a Matrix with a Unit Vector	1
Problems and Solutions	1
When I Knew Math Was Mine	1
A Third Real Solution to x=x−1, Not Really	1
Problems and Solutions	1
More on the Cauchy–Schwarz Inequality	1
The Infinitude of the Primes and Some Coloring Theorems	1
Five or Ten New Proofs of the Pythagorean Theorem	1
The Discrete Theorema Egregium	1
Sharp Effective Finite-Field Nullstellensatz	1
Yet Another Proof of the Strong Law of Large Numbers	1
Problems and Solutions	1
Summation Using an Expected Value Identity	1
Which Finite Rings Have the Most or Fewest Units?	1
100 Years Ago This Month in The American Mathematical Monthly	1
Reviews	1
A Lebesgue Integral Variant of the Additive Square Problem	1
Lagrange Points and the James Webb Space Telescope	1
Problems and Solutions	1
Following in Yiu’s Footsteps but on the Eisenstein Lattice	1
100 Years Ago This Month in The American Mathematical Monthly	1
Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions	1
The Eighty-Second William Lowell Putnam Mathematical Competition	1
Topology Meets Number Theory	1
Problems and Solutions	1

A Model for Birdwatching and other Chronological Sampling Activities	1
Editor’s Endnotes	1
100 Years Ago This Month in The American Mathematical Monthly	1
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything ElseShape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. By JordanEllen	1
100 Years Ago This Month in The American Mathematical Monthly	1
Sports Analytics Double Take: The Need for Multiple Perspectives on Data	1
The Poetry of Category Theory	1
Problems and Solutions	1
Euclidean Rings of S -integers in Complex Quadratic Fields	1
Parallelogram Law and Sum of Squares	1
Reviews	1
Discrete Calculus and Weighted Fibonacci and Tribonacci Sums	1
On the Divisibility of a Polynomial by One of its Derivatives	1
Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts	1
Abbott Dimension, Mathematics Inspired by Flatland	1
Integers as Sums of Four Tetrahedral Numbers and Eight Pentatope Numbers in One Identity	1
On the Primorial Counting Function	1
100 Years Ago This Month in The American Mathematical Monthly	1
Fourier Series for Nonperiodic Functions	1
Problems and Solutions	1
The Binomial Coefficient as an (In)finite Sum of Sinc Functions	1
The Genius of Gaudí: Geometry and Architecture	1
Problems and Solutions	1
Parallel Sections of a Convex Body by Planes Tangent to an Inner Sphere	1
The Simplest Unlimited-Player Game of Skill	1
A Shortcut to the Cauchy Integral Theorem	1
A Short and Elementary Proof of the Central Limit Theorem by Individual Swapping	1
George Bruce Halsted’s Non-Euclidean Pilgrimage to Hungary in 1896	1
A Derivation of the Infinitude of Primes	1
Water-Based Proof of Jensen’s Inequality	1
Polynomials Whose Zeros Are Powers of a Given Polynomial’s Zeros	1
A Geometric Summation of the Geometric Series	1
The Fundamental Theorem of Finite Fields: A Proof from First Principles	1
Faculty Seminar	1
Problems and Solutions	1
On the Cayley-Hamilton Theorem	1
Diagonalization Games	1
A Generalization of the Fan-Glicksberg Fixed Point Theorem	1
Rational Functions as Sums of Reciprocals of Polynomials	1
Embeddings of K 5 in the Torus	1
Problems and Solutions	1
Is AX = Y Possible with a Positive Definite A ?	0
100 Years Ago This Month in The American Mathematical Monthly	0
Triangle Inequalities Indexed by Graphs	0
Convex Bodies with Equipotential Circles	0
Problems and Solutions	0
An Equilateral Triangle of Side > n Cannot be Covered by n 2 + 1 Unit Equilateral Triangles Homothetic to it	0
Reviews	0
Correction	0
Problems and Solutions	0
Intrinsic Geometries of the Simple Group of Order 168	0
The Factor Ring Structure of Quadratic Principal Ideal Domains	0
The Mathematics of Crossword Puzzles: In Celebration of Karen Hunger Parshall	0
Divisibility Graphs and Modular Multiplication Tables	0
Newton’s Method Without Division	0
If Rm ≅ Rn must m = n?	0
The Powers of Certain Number-Theoretic Matrices	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Quixotic Proof of Fermat’s Two Squares Theorem for Prime Numbers	0
Euclid after Computer Proof-Checking	0
The Pentagonal Pizza Conjecture	0
A Special Form of Slower Divergent Series	0
Testing Whether a Table Defines a Group	0
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers	0
Solving Algebraic Equations by Completing Powers	0
An Elementary Proof of the Layer Cake Representation Theorem	0
A Friendly Guide to the Real Exponential Function	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Importance of Being Prime ⋆ , a Nontrivial Generalization for Nonunique Factorizations	0
Odd-Period Cycles of the Logistic Map	0
Invariance of the Area and Volume of Cycloid Surfaces and Trochoid Surfaces	0
An Arithmetic-Geometric Proof of the Arithmetic-Geometric Inequality	0
Ten Points on a Cubic	0
Using a SAT Solver to Find Interesting Sets of Nonstandard Dice	0
The Possible Asylum	0
A Conjecture on Primes in Arithmetic Progressions and Geometric Intervals	0
Reviews I Died for Beauty: Dorothy Wrinch and the Cultures of Science . By Marjorie Senechal, Oxford University Press, 2012. 312 pp., ISBN 978-0199732593, $57.00.	0
Freely Independent Coin Tosses, Standard Young Tableaux, and the Kesten–McKay Law	0
Problems and Solutions	0
Duelling Idiots and Abel Sums	0

A More Malicious Maitre d’	0
Problems and Solutions	0
Lucky Cars and the Quicksort Algorithm	0
Modeling & Optimization for Streaming Listening Demand	0
Archive Labeling Sequences	0
Sums of Two Squares Visualized	0
The Maximum Number of Appearances of a Word in a Grid	0
An Increasing Function with a Discontinuous Derivative	0
Reviews	0
AGM and Jellyfish Swarms of Elliptic Curves	0
A Remark on the Ratio of Consecutive Primes	0
Problems and Solutions	0
Complex Numbers as Powers of Transcendental Numbers	0
A Gauche Perspective on Row Reduced Echelon Form and Its Uniqueness	0
Wolstenholme’s Congruence for Lucas Sequences	0
Legendre’s Singular Modulus	0
A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode	0
Construction of an Iterated Function System on ℝ 2 whose Attractor is a QR Code	0
On 2025 and Other Torn Numbers	0
On the Complex Descartes Circle Theorem	0
A Simple Construction of Fat Cantor Sets	0
An Elementary Proof of Takagi’s Theorem on the Differential Composition of Polynomials	0
On Parking Functions and The Tower of Hanoi	0
The Birational Geometry of Ceva’s Theorem	0
An assessment model for proof comprehension in undergraduate mathematics	0
What Is the Shape of a Cupola?	0
An Upper Bound on the Size of Sidon Sets	0
The Simplest Polynomial Differential Systems in ℝ 3 Having an Invariant Sphere	0
Pythagorean Boxes and Quotients of Gaussian Integers	0
Cyclic Arithmetic and Combinatorial Operations	0
Travel in an Infinite Desert	0
The Intermediate Value Theorem for Linear Transformations	0
New Primality Criterion Based on Lucas Sequences	0
How to Tee a Hyperplane	0
Reviews	0
How Many Homeomorphisms are “Many Homeomorphisms”?	0
Problems and Solutions	0
You Probably Won’t Believe It, But 3(1+φ − φ−1) = 3!	0
Inscribing Spheres in Topologically Embedded Simplices	0
A Second Raabe’s Test and Other Series Tests	0
Spandrelized Tilings	0
Some Applications of the Maynard–Tao Theorem	0
Math Games With Bad Drawings: 75 Simple, Challenging, Go-Anywhere Games—And Why They Matter	0
On Nonnegativity of the Generalized Discriminants of Quadratics	0
Unlocking Your Bike the Easy Way	0
Gagliardo-Nirenberg-Sobolev Inequality: An Induction Proof	0
Reviews	0
Vieta’s Formula, the Fabius Function and the Partition Function	0
Reviews	0
Conway’s Spiral and a Discrete Gömböc with 21 Point Masses	0
Laws of Exponents by Differentiation	0
An Upper Bound on the Divisor Counting Function	0
Letter from the Editor	0
Frobenius Integrability, Automotive Blind Spots, Non-reversing Mirrors, and Panoramic Mirrors	0
Correction	0
What Do Networks and Elliptic Curves Have in Common?	0
Problems and Solutions	0
Collective Evolution Under Catastrophes	0
Diversity, Identity, and Data	0
Geometric Graphs with Exponential Chromatic Number and Arbitrary Girth	0
Reciprocity via Reciprocants	0
Calculating Prodigies in the Nineteenth Century: Science as Spectacle or Real Skill?	0
A Beautiful Inequality by Saint-Venant and Pólya Revisited	0
When Will (Game) Wars End?	0
Reviews	0
Approximating Complex Numbers by Roots of Integral Irreducible Polynomials	0
Celebrating Herbert Slaught’s “Romance of Mathematics”	0
Euler’s Inequality for Circumradius and Inradius	0
A Napoleon-like Theorem for Quadrilaterals	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reviews	0
A New Perspective on Impartial and Unbiased Apportionment	0
A Friendly Introduction to Path Algebras and Quiver Representations	0
Integration of Gauß-Type Functions in Finite Terms	0
The Paul R. Halmos–Lester R. Ford Awards for 2022	0
Ghostly Irrational Numbers	0
An Observation on Average Velocity	0
Factoring Variants of Chebyshev Polynomials of the First and Second Kinds with Minimal Polynomials of cos(2π/d)	0
Reviews Graph Theory in America: The First Hundred Years . By Robin Wilson, John J. Watkins, and David J. Parks, Princeton University Press, 2023. 320 pp., ISBN 978-0691	0
The Subseries are Dense in the Basel Problem	0
Regular Patterns of Quadratic Residues	0
Counting Zeros of Random Functions	0
An “Esoteric” Proof of Gelin-Cesàro Identity	0
From Abel’s Binomial Theorem to Cayley’s Tree Formula	0
On the Divisibility a! + b! | (a + b)!	0
N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium	0
The Poincaré Exponent and the Dimensions of Kleinian Limit Sets	0
Invariance of the Cauchy Family Under Linear Fractional Transformations	0
On the Topology of Punctured Spaces	0
Around the GCD of the Values of Two Polynomials	0
100 Years Ago This Month in The American Mathematical Monthly	0
Excavating and Analyzing Mathematics in the Mary Somerville Collection, Oxford	0
Encyclopedia of Knot Theory	0
A Pigeon Hole Proof of the Infinitude of Primes	0
Lagrange Inversion Formula by Induction	0