American Mathematical Monthly

Article	Citations
A Very Short Proof of the Hermite–Hadamard Inequalities	16
When Is a Puiseux Monoid Atomic?	13
New Properties of Triangular Orbits in Elliptic Billiards	9
Turning the Partition Crank	8
A Sharp Form of the Discrete Hardy Inequality and the Keller–Pinchover–Pogorzelski Inequality	6
The False Strategy Theorem: A Financial Application of Experimental Mathematics	5
A New View of Hypercube Genus	5
An Inequality Can Change Everything…	4
l’Hôpital’s Rule for Multivariable Functions	4
Guessing about Guessing: Practical Strategies for Card Guessing with Feedback	4
How to Cut a Cake Fairly: A Generalization to Groups	4
An Entropy Proof of the Arithmetic Mean–Geometric Mean Inequality	4
Exploring a Planet, Revisited	4
The Pentagonal Pizza Conjecture	4
On Experimental Mathematics and Mathematics Education	3
A Prime Primitive Root p of 2 p + 1 is a Sophie Germain Prime	3
A Short Proof of Fermat’s Two-square Theorem	3
Pollock’s Generalized Tetrahedral Numbers Conjecture	3
Containing All Permutations	3
Apéry Limits: Experiments and Proofs	3
Each Positive Rational Number Has the Form φ(m2)/φ(n2)	3
Disks in Curves of Bounded Convex Curvature	3
Unconditional Prime-Representing Functions, Following Mills	3
Navigating Around Convex Sets	3
Nontransitive Random Variables and Nontransitive Dice	3

The Bounded Convergence Theorem	3
Delicate Details of Filling Space	3
Euler and the Cubic Basel Problem	3
Fermat’s Last Theorem Implies Euclid’s Infinitude of Primes	3
Quasirandom Graphs and the Pantograph Equation	3
On a Nearly Forgotten Polynomial Result by P. Bohl	3
Delone Sets Generated by Square Roots	3
Factoring Variants of Chebyshev Polynomials of the First and Second Kinds with Minimal Polynomials of cos(2π/d)	2
Extremal Numbers of Cycles Revisited	2
Solution of an Odds Inversion Problem	2
A Generalization of Euler’s Limit	2
A Short, Elementary Introduction to the Exponential Function	2
What Type of Apollonian Circle Packing Will Appear?	2
Cutting a Cake Fairly for Groups Revisited	2
Analysis of Series and Products. Part 1: The Euler–Maclaurin Formula	2
Three Symmetric Double Series by Telescoping	2
Length-Preserving Directions and Some Diophantine Equations	2
How (Not) to Cut Your Cheese	2
A Water-Based Proof of the Cauchy–Schwarz Inequality	2
Note on Dirichlet’s Sinc Integral	2
Simpson’s Paradox, Visual Displays, and Causal Diagrams	2
Wald’s Identity and Geometric Expectation	2
The Game of Cycles	2
A Quick Proof of the Order-Extension Principle	2
The Abel–Ruffini Theorem: Complex but Not Complicated	2
Cauchy–Schwarz Inequality for Differences Revisited	2
Moon in a Puddle and the Four-Vertex Theorem	2
Separability of a Metric Space Is Equivalent to the Existence of a Borel Measure	2
Between the Cracks: Filling Space with Polygonal Shapes	2
A Cauchy–Schwarz Type Inequality for Differences	2
A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem	2
Cubes and Boxes Have Rupert’s Passages in Every Nontrivial Direction	2
Countable Metric Spaces Without Isolated Points	2
Classifying Groups With a Small Number of Subgroups	1
Green’s Function for the Neumann–Poisson Problem on n-Dimensional Balls	1
Morikawa’s Unsolved Problem	1
Yet Another Proof of the Strong Law of Large Numbers	1
On the Automorphism Group of Direct Products of Groups with Finite Exponent	1
Tangent Spheres of Tetrahedra and a Theorem of Grace	1
Some Applications of the Maynard–Tao Theorem	1
A Short and Elementary Proof of the Central Limit Theorem by Individual Swapping	1
Composites in the Ulam Spiral	1
Minimax Theorem Revisited	1
How to Tee a Hyperplane	1
On Parking Functions and The Tower of Hanoi	1
Crystallographic Groups, Strictly Tessellating Polytopes, and Analytic Eigenfunctions	1
Using Ultrafilters to Prove Ramsey-type Theorems	1
Integral Recurrences from A to Z	1
Reducing Multiple Integrals of Beukers’s Type	1
When Is a Continuous Bijection a Homeomorphism?	1

PROBLEMS AND SOLUTIONS	1
The Power of the Half Power	1
Null Subsets of All Sizes Inside Vitali Sets	1
A Fractal Eigenvector	1
Chords of an Ellipse, Lucas Polynomials, and Cubic Equations	1
Bijective Proofs of Proper Coloring Theorems	1
The Simplest Unlimited-Player Game of Skill	1
Euclid after Computer Proof-Checking	1
A New Perspective on Impartial and Unbiased Apportionment	1
Morley Trisectors and the Law of Sines with Reflections	1
An Entire Function Connected with the Approximation of the Golden Ratio	1
Escaping an Infinitude of Lions	1
Gambling Under Unknown Probabilities as Proxy for Real World Decisions Under Uncertainty	1
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio	1
Problems and Solutions	1
Gardener’s Hyperbolas and the Dragged-Point Principle	1
A Good Question Won’t Go Away: An Example of Mathematical Research	1
Discriminants of Quadratics Generalized	1
Sums of Powers in Large Finite Fields: A Mix of Methods	1
Encyclopedia of Knot Theory	1
What’s Special about the Perfect Number 6?	1
A Gambler that Bets Forever and the Strong Law of Large Numbers	1
Browder’s Theorem through Brouwer’s Fixed Point Theorem	1
A Uniform Proof of the Finiteness of the Class Group of a Global Field	1
Problems and Solutions	1
Leibniz, Newton, and Cauchy: A Complex Relationship	1
What Is the Shape of a Cupola?	1
Computing Moore–Penrose Inverses with Polynomials in Matrices	1
Summation Using an Expected Value Identity	1
On Certain Probabilistic Properties of Polynomials over the Ring of p-adic Integers	1
Are There More Finite Rings than Finite Groups?	1
Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model	1
A Stochastic Approach to Eulerian Numbers	1
Sums of Finite Sets of Integers, II	1
A Brief Discourse on Hausdorff Dimension and Self-similarity	1
A Communicating-Vessels Proof of Hölder’s Inequality	1
Perfect Metric Spaces of Increasingly Large Cardinality	1
Another Proof of the Infinitude of Primes	1
Down with Weierstrass!	1
Problems and Solutions	1
An Upper Bound on the Size of Sidon Sets	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
On Arithmetic Progressions of Powers in Cyclotomic Polynomials	1
Perron’s Theorem in an Hour	1
Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions	1
Invariance of the Length and the Area of Cycloids	1
Odds Inversion Problem With Replacement	1
Optimizing for the Rupert Property	1
N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium	1
The Geodesics for Poincaré’s Half-Plane: A Nonstandard Derivation	1
A Geometric Summation of the Geometric Series	0
100 Years Ago This Month in the American Mathematical Monthly	0
A Plethora of Polynomials: A Toolbox for Counting Problems	0
Reviews	0
A Friendly Introduction to Path Algebras and Quiver Representations	0
On Some Localizations and Their Relation to Quotients	0
Discrete Morse Theory by Nicholas Scoville	0
Problems and Solutions	0
Math Games With Bad Drawings: 75 Simple, Challenging, Go-Anywhere Games—And Why They Matter	0
The Paul R. Halmos–Lester R. Ford Awards for 2022	0
The Altitudes of a Triangle	0
Travel in an Infinite Desert	0
PROBLEMS AND SOLUTIONS	0
A Nonzero Sequence All of Whose Discrete Moments Are Equal to Zero	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Factor Ring Structure of Quadratic Principal Ideal Domains	0
Ten Points on a Cubic	0
Polynomial Approximations to Continuous Functions	0
Problems and Solutions	0
Positional Voting and Doubly Stochastic Matrices	0
Remark on Cauchy–Schwarz Inequality for Differences	0
Packing Density of Combinatorial Settlement Planning Models	0
Problems and Solutions	0
Where Have All the Grasshoppers Gone?	0
A Law of Conservation of Symbols	0
100 Years Ago This Month in The American Mathematical Monthly	0
Introduction to the Special Issue	0
Numerical Semigroups and the Game of Sylver Coinage	0
100 Years Ago This Month in The American Mathematical Monthly	0
Playing Mastermind with Wordle-like Feedback	0

Problems and Solutions	0
Infinitely Many Twin Prime Polynomials of Odd Degree	0
Counting Parity Palindrome Compositions	0
Problems and Solutions	0
Following in Yiu’s Footsteps but on the Eisenstein Lattice	0
Pentagram Configurations for Pentagons and Hexagons	0
Gaussian Binomial Coefficients in Group Theory, Field Theory, and Topology	0
The Eightieth William Lowell Putnam Mathematical Competition	0
An Elementary Proof of Takagi’s Theorem on the Differential Composition of Polynomials	0
Reviews	0
An Arithmetic Proof of a Theorem of Chan, Long, and Yang	0
Which Finite Rings Have the Most or Fewest Units?	0
On a Classic Problem in the Calculus of Variations: Setting Straight Key Properties of the Catenary	0
A Combinatorial Proof of a Symmetric Group Character Involution	0
Polynomially Isometric Matrices in Low Dimensions	0
100 Years Ago This Month in The American Mathematical Monthly	0
The Mathematical Association of America Prime	0
Factorization of Perplex Integers	0
The Distribution of Fibonacci Numbers Modulo Primes	0
Reviews	0
Random Walks, Directed Cycles, and Markov Chains	0
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics	0
100 Years Ago This Month in The American Mathematical Monthly	0
Another Alternating Analogue of Euler’s Constant	0
What Do Networks and Elliptic Curves Have in Common?	0
Complex Numbers as Real Continued Fractions	0
In Search of Comrade Agronomof: Some Tribonacci History	0
Metric Spaces where Geodesics are Never Unique	0
On Erdős’s Proof of the Existence of Cages	0
Reviews	0
Reviews An Introduction to the Circle Method . By M. Ram Murty & Kaneenika Sinha, American Mathematical Society, 2023. 258 pp., ISBN 978-1-4704-7203-0, $59.00.	0
The Theorem of the Primitive Element	0
Reviews	0
100 Years Ago This Month in The American Mathematical Monthly	0
My Friend Abe Shenitzer	0
Problems and Solutions	0
A Statistical Proof of Chebyshev’s Sum Inequality	0
The Natural Logarithm Modulo 2	0
The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality	0
169 and Sums of Positive Squares	0
100 Years Ago This Month in The American Mathematical Monthly	0
Dubious Identities: A Visit to the Borwein Zoo	0
A Second Look at the Second Ratio Test	0
Community and Belonging in Mathematics*	0
An Equality Underlying Hardy’s Inequality	0
A Jeep Crossing a Desert of Unknown Width	0
On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement	0
Lucky Cars: Expected Values and Generating Functions	0
100 Years Ago This Month in The American Mathematical Monthly	0
Foster, Turán, and Neighbors	0
Problems and Solutions	0
Editor’s Endnotes	0
Billiard Circuits in Quadrilaterals	0
Regular Patterns of Quadratic Residues	0
Monthly Referees for 2023	0
A Note on the Geometry of Figurate Numbers	0
Integration using Schwinger Parametrization	0
Editor’s Endnotes	0
x + y: A Mathematician’s Manifesto for Rethinking Gender	0
On the Topology of Punctured Spaces	0
The Martin Gardner Polytopes	0
A Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma	0
Extremal Values of Pi	0
The Concentration of the Product of Exponentials Around the Exponential of the Sum	0
The Paul R. Halmos–Lester R. Ford Awards for 2021	0
Stickelberger’s Discriminant Theorem for Algebras	0
Commutators in the Rubik’s Cube Group	0
The Fundamental Theorem of Algebra Via Newton’s Identities	0
Reviews	0
Reviews	0
100 Years Ago This Month in The American Mathematical Monthly	0
Sharp Effective Finite-Field Nullstellensatz	0
Odd-Period Cycles of the Logistic Map	0
Reflections on Equidistant Sets	0
Six Proofs of the Fáry–Milnor Theorem	0
Mathematics for Human Flourishing	0
Ohm My: An Electrifying Method of Summing Arithmetic Sequences	0
Problems and Solutions	0
Problems and Solutions	0
Tessellations: Mathematics, Art, and Recreation	0
Problems and Solutions	0
Paying Our Way Out of a Crisis	0
A Simple Construction of Fat Cantor Sets	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reviews	0
Euler’s Inequality for Circumradius and Inradius	0
Zero Exclusion Sectors for Some Polynomials with Structured Coefficients	0
Letter from the Editor	0
A Number System with Base	0
Problems and Solutions	0
The Mathematical Community Working To Create Better (And Free!) Textbooks	0
Problems and Solutions	0
Six Houses and Three Utilities on A Coffee Mug	0
PROBLEMS AND SOLUTIONS	0
Tiling with Monotone Polyominos	0