American Mathematical Monthly

Article	Citations
When Is a Puiseux Monoid Atomic?	15
New Properties of Triangular Orbits in Elliptic Billiards	9
A Sharp Form of the Discrete Hardy Inequality and the Keller–Pinchover–Pogorzelski Inequality	8
The False Strategy Theorem: A Financial Application of Experimental Mathematics	7
How to Cut a Cake Fairly: A Generalization to Groups	6
A New View of Hypercube Genus	5
Quasirandom Graphs and the Pantograph Equation	5
The Pentagonal Pizza Conjecture	4
An Inequality Can Change Everything…	4
A Prime Primitive Root p of 2 p + 1 is a Sophie Germain Prime	4
Exploring a Planet, Revisited	4
A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem	4
Guessing about Guessing: Practical Strategies for Card Guessing with Feedback	4
On Experimental Mathematics and Mathematics Education	3
Euler and the Cubic Basel Problem	3
Cutting a Cake Fairly for Groups Revisited	3
On a Nearly Forgotten Polynomial Result by P. Bohl	3
Three Symmetric Double Series by Telescoping	3
Delicate Details of Filling Space	3
Fermat’s Last Theorem Implies Euclid’s Infinitude of Primes	3
Containing All Permutations	3
Packing Density of Combinatorial Settlement Planning Models	3
Apéry Limits: Experiments and Proofs	3
Simpson’s Paradox, Visual Displays, and Causal Diagrams	3
Pollock’s Generalized Tetrahedral Numbers Conjecture	3

Nontransitive Random Variables and Nontransitive Dice	3
Extremal Numbers of Cycles Revisited	3
Separability of a Metric Space Is Equivalent to the Existence of a Borel Measure	3
Gambling Under Unknown Probabilities as Proxy for Real World Decisions Under Uncertainty	2
Cubes and Boxes Have Rupert’s Passages in Every Nontrivial Direction	2
Countable Metric Spaces Without Isolated Points	2
Cauchy–Schwarz Inequality for Differences Revisited	2
Gardener’s Hyperbolas and the Dragged-Point Principle	2
Note on Dirichlet’s Sinc Integral	2
What Type of Apollonian Circle Packing Will Appear?	2
An Upper Bound on the Size of Sidon Sets	2
The Game of Cycles	2
The Abel–Ruffini Theorem: Complex but Not Complicated	2
Length-Preserving Directions and Some Diophantine Equations	2
Moon in a Puddle and the Four-Vertex Theorem	2
Computing Moore–Penrose Inverses with Polynomials in Matrices	2
A Cauchy–Schwarz Type Inequality for Differences	2
Crystallographic Groups, Strictly Tessellating Polytopes, and Analytic Eigenfunctions	2
Analysis of Series and Products. Part 1: The Euler–Maclaurin Formula	2
Factoring Variants of Chebyshev Polynomials of the First and Second Kinds with Minimal Polynomials of cos(2π/d)	2
How (Not) to Cut Your Cheese	2
Solution of an Odds Inversion Problem	2
A Generalization of Euler’s Limit	2
N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium	2
An Extension of Ceva’s Theorem to n-Simplices	1
On Arithmetic Progressions of Powers in Cyclotomic Polynomials	1
Composites in the Ulam Spiral	1
Discriminants of Quadratics Generalized	1
The Power of the Half Power	1
Odds Inversion Problem With Replacement	1
Problems and Solutions	1
Summation Using an Expected Value Identity	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
Euclid after Computer Proof-Checking	1
On the Tower Factorization of Integers	1
Morley Trisectors and the Law of Sines with Reflections	1
Classifying Groups With a Small Number of Subgroups	1
Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model	1
A Brief Discourse on Hausdorff Dimension and Self-similarity	1
Another Proof of the Infinitude of Primes	1
Problems and Solutions	1
Following in Yiu’s Footsteps but on the Eisenstein Lattice	1
Problems and Solutions	1
Lucky Cars and the Quicksort Algorithm	1
Minimax Theorem Revisited	1
Problems and Solutions	1
Vector Fields with Continuous Curl but Discontinuous Partial Derivatives	1
On the Complex Descartes Circle Theorem	1
Perron’s Theorem in an Hour	1
Using Ultrafilters to Prove Ramsey-type Theorems	1

The Fundamental Theorem of Finite Fields: A Proof from First Principles	1
Reducing Multiple Integrals of Beukers’s Type	1
Regular Polygons and Central Moments	1
Optimizing for the Rupert Property	1
Analytic Continuations of Character and Alternating Tornheim Zeta Functions	1
The Geodesics for Poincaré’s Half-Plane: A Nonstandard Derivation	1
Bijective Proofs of Proper Coloring Theorems	1
What’s Special about the Perfect Number 6?	1
Odd-Period Cycles of the Logistic Map	1
Polynomials Consisting of Quadratic Factors with Roots Modulo Any Positive Integer	1
Problems and Solutions	1
The Simplest Unlimited-Player Game of Skill	1
Some Applications of the Maynard–Tao Theorem	1
Morikawa’s Unsolved Problem	1
A Short and Elementary Proof of the Central Limit Theorem by Individual Swapping	1
How to Tee a Hyperplane	1
A Quick Route to Unique Factorization in Quadratic Orders	1
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio	1
Optimizing and Factorizing the Wilson Matrix	1
Sums of Two Squares Visualized	1
Escaping an Infinitude of Lions	1
Encyclopedia of Knot Theory	1
The Poincaré Exponent and the Dimensions of Kleinian Limit Sets	1
Integral Recurrences from A to Z	1
Sums of Powers in Large Finite Fields: A Mix of Methods	1
A Communicating-Vessels Proof of Hölder’s Inequality	1
On Parking Functions and The Tower of Hanoi	1
A Gambler that Bets Forever and the Strong Law of Large Numbers	1
Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions	1
Problems and Solutions	1
A Fractal Eigenvector	1
Leibniz, Newton, and Cauchy: A Complex Relationship	1
What Is the Shape of a Cupola?	1
A Uniform Proof of the Finiteness of the Class Group of a Global Field	1
Yet Another Proof of the Strong Law of Large Numbers	1
Counting Zeros of Random Functions	1
Reviews	1
A New Perspective on Impartial and Unbiased Apportionment	1
A Characterization of Cesàro Convergence	1
On the Automorphism Group of Direct Products of Groups with Finite Exponent	1
Tangent Spheres of Tetrahedra and a Theorem of Grace	1
A Good Question Won’t Go Away: An Example of Mathematical Research	1
Reviews	1
Perfect Metric Spaces of Increasingly Large Cardinality	1
An Observation on Average Velocity	1
From Abel’s Binomial Theorem to Cayley’s Tree Formula	1
Browder’s Theorem through Brouwer’s Fixed Point Theorem	1
Sums of Finite Sets of Integers, II	1
Six Proofs of the Fáry–Milnor Theorem	0
169 and Sums of Positive Squares	0
100 Years Ago This Month in The American Mathematical Monthly	0
Problems and Solutions	0
Zero Exclusion Sectors for Some Polynomials with Structured Coefficients	0
Problems and Solutions	0
Dubious Identities: A Visit to the Borwein Zoo	0
Gaussian Binomial Coefficients in Group Theory, Field Theory, and Topology	0
Infinitely Many Twin Prime Polynomials of Odd Degree	0
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics	0
The Fundamental Theorem of Algebra Via Newton’s Identities	0
On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement	0
100 Years Ago This Month in The American Mathematical Monthly	0
Six Houses and Three Utilities on A Coffee Mug	0
Polynomially Isometric Matrices in Low Dimensions	0
Reviews	0
Problems and Solutions	0
Reviews	0
A Thābit-like Extension of the Pythagorean Theorem	0
Conway’s Spiral and a Discrete Gömböc with 21 Point Masses	0
On a Classic Problem in the Calculus of Variations: Setting Straight Key Properties of the Catenary	0
Problems and Solutions	0
Editor’s Endnotes	0
A Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma	0
Problems and Solutions	0
PROBLEMS AND SOLUTIONS	0
100 Years Ago This Month in the American Mathematical Monthly	0
Z[−5]: Halfway to Unique Factorization	0
A Telescopic Proof of Cayley’s Formula	0
Polynomial Approximations to Continuous Functions	0
A Combinatorial Proof of a Symmetric Group Character Involution	0
Travel in an Infinite Desert	0

Metric Spaces where Geodesics are Never Unique	0
A Fair Shake: How Close Can The Sum Of n -Sided Dice Be To A Uniform Distribution?	0
My Friend Abe Shenitzer	0
Pentagram Configurations for Pentagons and Hexagons	0
Tiling with Monotone Polyominos	0
Introduction to the Special Issue	0
Positional Voting and Doubly Stochastic Matrices	0
Reviews	0
Reviews	0
Tessellations: Mathematics, Art, and Recreation	0
Reviews	0
Problems and Solutions	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Statistical Proof of Chebyshev’s Sum Inequality	0
Euler’s Inequality for Circumradius and Inradius	0
A Jeep Crossing a Desert of Unknown Width	0
On Some Localizations and Their Relation to Quotients	0
A Friendly Introduction to Path Algebras and Quiver Representations	0
Community and Belonging in Mathematics*	0
Playing Mastermind with Wordle-like Feedback	0
Stickelberger’s Discriminant Theorem for Algebras	0
Regular Patterns of Quadratic Residues	0
The Mathematical Community Working To Create Better (And Free!) Textbooks	0
Problems and Solutions	0
Which Finite Rings Have the Most or Fewest Units?	0
Five or Ten New Proofs of the Pythagorean Theorem	0
Reviews	0
Editor’s Endnotes	0
Ten Points on a Cubic	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Dynamic Kelly Criterion for Games with a Maximum Payout	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
x + y: A Mathematician’s Manifesto for Rethinking Gender	0
The Paul R. Halmos–Lester R. Ford Awards for 2023	0
The Distribution of Fibonacci Numbers Modulo Primes	0
Commutators in the Rubik’s Cube Group	0
Closed Geodesics on the Mylar Balloon Shape	0
What Do Networks and Elliptic Curves Have in Common?	0
An Arithmetic Proof of a Theorem of Chan, Long, and Yang	0
100 Years Ago This Month in The American Mathematical Monthly	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reviews	0
An Equality Underlying Hardy’s Inequality	0
Another Alternating Analogue of Euler’s Constant	0
Sharp Effective Finite-Field Nullstellensatz	0
A Generalization of Wayment’s Mean Value Theorem for Integrals	0
Problems and Solutions	0
A Note on the Geometry of Figurate Numbers	0
Where Have All the Grasshoppers Gone?	0
The Natural Logarithm Modulo 2	0
The Theorem of the Primitive Element	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality	0
An Elementary Proof of Takagi’s Theorem on the Differential Composition of Polynomials	0
Reviews	0
Lucky Cars: Expected Values and Generating Functions	0
A Second Look at the Second Ratio Test	0
Ohm My: An Electrifying Method of Summing Arithmetic Sequences	0
Counting Parity Palindrome Compositions	0
Problems and Solutions	0
Integration using Schwinger Parametrization	0
The Paul R. Halmos–Lester R. Ford Awards for 2022	0
Letter from the Editor	0
On Erdős’s Proof of the Existence of Cages	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Plethora of Polynomials: A Toolbox for Counting Problems	0
Foster, Turán, and Neighbors	0
Add Nihilo	0
Monthly Referees for 2023	0
How Long Can k -Göbel Sequences Remain Integers?	0
Reviews	0
A Geometric Summation of the Geometric Series	0
Problems and Solutions	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Factor Ring Structure of Quadratic Principal Ideal Domains	0
Problems and Solutions	0
The Concentration of the Product of Exponentials Around the Exponential of the Sum	0
Are There More Finite Rings than Finite Groups?	0
New Primality Criterion Based on Lucas Sequences	0
In Search of Comrade Agronomof: Some Tribonacci History	0
Reviews	0
Billiard Circuits in Quadrilaterals	0
Extremal Values of Pi	0
The Altitudes of a Triangle	0
On Liouville’s Theorem for Conformal Maps	0
Reflections on Equidistant Sets	0
A Number System with Base	0
Remark on Cauchy–Schwarz Inequality for Differences	0
Problems and Solutions	0
Problems and Solutions	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Simple Construction of Fat Cantor Sets	0
Factorization of Perplex Integers	0
A Law of Conservation of Symbols	0
100 Years Ago This Month in The American Mathematical Monthly	0