This is a combined list of all the articles currently available on this site.Sequences Formed By Rounding The Twelve-Step Cycle of 1/(sin(x)cos(x)) Symmetric Pseudoprimes Digit Reversal Sums Leading to Palindromes Min-Energy Configurations of Electrons On A Sphere The Sum of the Prime Factors of N Smith Numbers and Rhonda Numbers Sequence Partitionable Into Powers of 2 or 3 Fermat's Last Theorem for Cubes Tangents, Exponentials, and PI Atlantic City Method For Computing PI Unification of Eulerians and Binomials Can Schrodinger's Cat Factor Numbers? Why z Is Not a Prime Power in z^p = x^p + y^p Zeisel Numbers Identities for Linear Recurring Sequences Summations and Recurrences Optimizing Your Wife Thinking Outside the Triangle Sum-of-Digits Iterations Maximizing A Symmetrical Function On Solutions of n!+1 = x^2 Random High-Low Searching Eulerians as Weighted Binomial Coefficients The Dartboard Sequence Poisson Processes and Queues Finite Subgroups of the Mobius Group The Dullness of 1729 Highly Wilsonian Primes Dedekind's Problem Permutation Loops Legendre's Prime Number Conjecture Probabilities With Renaming Finding Roots From Newton's Sums Multiple Linear Regression At Least One Girl Parabola Through Four Points Archimedes and the Square Root of 3 Polyomino Enumerations Divisors of an n-term Geometric Series Congruences on 4th Order Recurrences Ratio Populations Piano Keys No Four Squares In Arithmetic Progression Integrating the Bell Curve Differences Between Normal Samples The Collector's Problem Sum of Divisors Equals a Power of 2 Bertelsen's Number Sandford's Elevator Tables of 1 to N with Equal Columns The Coin in Three Fountains Euclid's Plan and Proposition 6 Geophysical Altitudes Generalized Mediant Intersecting Boats Generalized Birthday Problem (N Items in M Bins) Numeri Idonei Sequences With No Arithmetic Progressions Cutting Self-Similar Pentagons A Primality Criterion Meeting Combinations and Interval Graphs The Limit Paradox Can n Divide !n ? Asymptotic Approach to 2D Arrays Prisca Sapientia Iterated Logarithmic Functions A Mass and Spring System in Motion Pythagoras On Dot and Cross Products Diophantine Walk-a-thon Sums of Three Cubes Why Calculus? Congruences Involving the Totient Function Grazing Goats The Jewel of Arithmetic: Quadratic Reciprocity Distinct Point Sets With Same Distances A Conjecture On The Fermat Function Periods of Fibonacci Sequences mod m Curvature of Linear Interpolation Mayan Numeration Cyclic Divisibility Independence and Negation Infinitely Many Rhondas The Gambler's Ruin Geometric Dot Products and Digit Reversals Root-Matched Recurrences For DiffEQs A Procrustean Protocol Infinite Products and a Tangent Fan Boolean Expansion as Linear Interpolation Sighting Gravity Additive and Multiplicative Partitions Powers of Primes Dividing Factorials Dice Rolling A Given Sum Generating the Monotone Boolean Functions Coloring The Edges of an Icosahedron Platonic Solids and Plato's Theory of Everything Sums of Powers in Terms of Symmetric Functions Cumulative Permutation Sequences On Ptolmey's Theorem Binary Games Evidence for Goldbach Berkeley and the Infidel Zero-Order Remainders Powers Differing By 1 (Catalan) Barlow's Observation Computation is Exclusive Partitions into Consecutive Integers Fibonacci, 1/89, And All That The Speed of Sound Perpendicular Regression Of A Line Polynomials For Sums of Square Roots Hypocycloidal Engine Apollonius' Tangency Problem Gravitational Slingshot Minimum Difference Function Intrinsic Wobble of Spinning Objects Inverse-Square Forces and Orthogonal Polynomials Gauss' Lemma Without Divisibility Arguments Dual Failures with General Densities Sliding Ladders in the Abstract Newton's Birth Date and the Anni Mirabiles Weibull Analysis What is Fuzzy Logic? Meeting Probabilities A Better Lottery? Product Divisible By Sum of Squares Lucas Pseudoprimes Eigenvalue Problems and Matrix Invariants Center of Gravity With Integer Coordinates Iterated Means de Sitter's Binary Apparitions Evaluating Probabilities of Boolean Events On x^2 + y^2 = z^4, x + y = w^2 Zeta Function and Harmonic Series Continuous Turing Machines The Guest Star Recurrences For Harmonic Sums Saturnday, Sunday, Moonday Newton's Proposition LXXI Fractal Logic Implicit Means What Mirrors Do Bayesian Balls Infinite Descent versus Induction Ptolemy's Orbit Square Roots by Pencil and Paper Sums of Consecutive Nth Powers Equal to an Nth Power Exponential Iteration Quasi-Groups Reverse Greed for Unit Fractions Galileo's Anagrams and the Moons of Mars Aliasing and Uncertainty The Golden Pentagon A Mersenne Coincidence Franklin's Magic Squares Did Archimedes Know Gauss-Bonnet? Primes of the Form 2^(k-1) + k Zeno's Fifth Paradox Square Triangular Numbers Functions With No Zero Derivatives Planetary Alignment A Quasi-Periodic Sequence Volume of n-Spheres and the Gamma Function The 450 Pound Problem (x^3 + y^3 = 6z^3) The Factorial Number System String Algebra Is This a Prime? The Half-Totient Tree Trisection On A Budget The Lemniscate and Spacetime The Five Squarable Lunes Interleaving Ad Infinitum Loci of Equi-angular Points Entangled Choices 3->3 Mapping With No Crossed Lines The Statistics of Counterintelligence High Order Integration Schemes The No-Curvature Interpretation of GR Frequency Response of First-Order Lag Remembering Socrates The Revisionist FAQ The Bulging Earth Pseudoprimes For x^2 - 4x - 9 Primes In the Decimal Expansion of Pi In Defense of Base-Related Problems Radical Expression For cos(2pi/7) Interference or Refraction? Closed Forms For the Logistic Map The Prismoidal Formula Ancient Square Roots On f(x^2+y^2) = f(x)^2 + f(y)^2 Harmonia Mensurarum Limit Cycles of xy (mod x+y) Coprime Partitions Fermat's Fallibility Heron's Formula and Brahmagupta's Generalization A Rotating Disk in Translation Cyclical Partition Sequences Balls In Bins The Y10K Problem, Pascal's Wager, and Petersberg Net Area and Green's Theorem Sublime Numbers Roemer's Hypothesis More Results on the Form xy (mod x+y) The Shortest Path To Trigonometric Identities Do We Really Need Eigen Values? Generating Function For Eulerian Numbers Proving Algebraic Inequalities One-One Mapping of Reals and Sequences Phase, Group, and Signal Velocity Potential Flow and d'Alembert's Paradox A Knot of Congruences On x^2 + y^3 = z^6 The Laplace Equation and Harmonic Functions Series Solution of Non-Linear Equation Probabilities and Velocities Dialogues The Orbit of Triangles Translating Aristotle Integrating Factors The Filter Of Observation A Method Of Factoring Based On 1/N The Distribution of Perfection The Metamorphosis of Judas Iscariot Choice Without Context? Heron's Formula for Tetrahedrons Rolling Spheres and Cones Precession in a Circle A More Immortal Atlas On x^3 - x + y^3 - y = z^3 - z Factoring Convex Figures Restless Mass Fermat's Last Theorem for Quadratic Integers Pythagoras' Choice Two Geophysical Coincidences Quadratic Congruences Inside a Tetrahedron Quantum Interactions On Null Surfaces Accidental Melodies Magnetism and Earnshaw's Theorem Why Was Michelson Surprised? Huygens' Principle Recurrences and Pell Equations Complexity in Stars Compressor Stalls and Mobius Transformations Photons, Neutrinos, And Their Anti-Particles Series Solutions of the Wave Equation Leibniz's Rule Lead-Lag Frequency Response Twin Times The Wave Equation and Permutation of Rays Continued Fractions for e Leaning Ladders Old Notes on Curvature Differently Perfect Iterative Isoscelizing Reflecting on the Geometric Mean Analytic Functions, The Magnus Effect, and Wings Tilting Pencils A Barrel of Colors and Null Outcomes No Equilateral Triangles on a Chess Board Reconstructing Brouwer Simple Complex Quadratic Fields Exponential Partitions Detecting Squares The Four Color Theorem Combining Probabilities Convoluting Arrays Casting Out Nines Napoleon's Theorem Regular Polygonal Arrangements A Special Property of 151 Retrograde Moon? Pierre Gassendi, Mercurius in Sole Visus Numbers Expressible As (a^2 - 1)(b^2 - 1) The Shape of Coincidence Angular Angst Newtonian Gravity In Curved Space Sums of Powers Orbits and Perturbations Hero and Fermat on Receding Mirrors True, Equivalent, and Calibrated Airspeeds Mean Distance from Vertex to Interior of Plane Figures Bernoulli Numbers and Harmonic Series On Even Fibonacci Numbers Concordant Forms The e in Petersburg Fermat's Infinite Descent If ab+1, ac+1, bc+1 are squares,... Galois Groups Squares in Arithmetic Progression (mod p) Hail Encounters Inverse Square Weighted Interpolation The Fundamental Theorem For Palindromic Polynomials Solving Magic Squares Reducing Quartics to Cubics Annuities With Inflation Negative Numbers Random Triangles Two In the Shop Relative Rain Benford's Law On 13 Bridges Polynomials From Pascal's Triangle On m = sqrt(sqrt(n) + sqrt(kn+1)) Hermitian Matrices A Primer On Special Relativity A Budget of Barn Poles The Complex Domain of Probability The Determinants of 4x4 Magic Squares Acute Problem Self-Similar Reverse-Sum Sequences Proof That PI is Irrational Intersections of Polynomials Unit Fractions and Fibonacci Waring's Problem Seeking Prime Repunits Convergence of Series (How NOT to Prove PI Irrational) The Two Ohm Problem BASIC Program for Finding Pseudoprimes Importance of Being Urnest (B Balls, K Colors, N Urns) The Meanings of Catalan Numbers Cross-Linear Interpolation Distances In Bounded Regions Timely Confessions Infinite Parallel Redundancy N Points On Sphere all in One Hemisphere Main Daigonals and Euler's Totient Pent Up Ratios Differential Operators and the Divergence Theorem Two Properties of Markov Models Unit Fraction Partitions Given Primes p,q, Find Pseudoprime pqr N = (x^2 + y^2)/(1+xy) is a Square Leibniz On Computers Markov Models of Dual-Redundant Systems Balls In Bins With Limited Capacity Evaluate the Infinite Sum of n^2/(1+n^3) Black Holes, Event Horizons, and the Universe Egyptian Unit Fractions Bernoulli Trials Embedding Non-Euclidean Spaces in Euclidean Spaces Archimedes on Spheres and Cylinders Two-Dimensional Bernoulli Trials Perrin's Sequence Proof of Generalized Little Theorem of Fermat Is Arithmetic Consistent? Minimizing the Denominators of Unit Fraction Expansions Sphere Packing in Curved 3D Space Open-Loop and Closed-Loop Markov Models Equation of a Triangle 414298141056 Quarto Draws Suffice! Four Cubed (Complete Projection Cubes) A Mirror to Physics Bit-String Orbits Under Rotate-XOR Enumerating the Partition Transform Cycles Farey Series Pythagorean Graphs On General Palindromic Numbers Sequences of Characters in Random Strings Recurrence Relations for Ordinary Differential Equations Reflective and Cyclic Sets of Primes Fermat and Publication Representing Sets of Pure Order Interfering With PI The Longitude of Lewis and Clark On Case 1 of Fermat's Last Theorem Uniform Squares A Random Walk Through PI Botches, Failures, and Successes Cantor's Diagonal Proof Certainty In Mathematics Machin's Merit Theories and Interpretations Weighing the Evidence Progress on Sum of Prime Factors Function Dialogue On Mathematical and Physical Knowledge Permutation Puzzles Quintisection of an Angle Quadrilateral In a Circle Integer Sequences Related To PI The Ordering of Interactions Computing the Partitions of n Explanation of the Euclidean Algorithm Series Within Parallel Resistance Networks Galileo's Forgotten Leap Two Proofs for a Five Point Star Golf Tournaments, Polyhedra, and Latin Squares The Pigeon Hole Principle Generating Functions for Point Set Distances Harmonic Sums of Integers With k Binary 1's Are All Triangles Isosceles? Volume Under a Triangle Clouds, Shy Squares, and Diophantus Infinite Distance In Finite Time White Ravens and Black Swans Hipparchus on Coumpound Statements Invariance, Contravariance, Covariance Smallest Quad With Integer Sides, Perp Diags Proof that e is Irrational Constructible Points and Coverable Points Gravity of a Torus Anti-Carmichael Pairs Schizophrenic Numbers The Moon Always Falls Toward the Sun Irreducibility Criteria Newtonian and Relativistic Conservation Laws Napoleonic Vectors Accelerating In Place Is the World Provably Indeterminate? On the Density of Some Exceptional Primes Path Lengths and Coordinates Preserving the Wave The Fundamental Anagram of Calculus Higher-Order Wave Equations and Matter Waves Cellular Automata Magic Square of Squares A Quarky Formula for Volume of Parallelpiped On the Cumulative Results of Quantum Measurements Bell Tests and Biased Samples Impossible Strings for Cellular Automata Born Rigidity, Acceleration, and Inertia Round-Robin Ties Piero della Francesca's Tetrahedron Formula From Euclid to Gregory Expected Length of Random Hi/Low Search Orthomagic Square of Squares On Random Chords Automedian Triangles, Eigen Vectors, and Magic Squares Derangements and Generalizations Gamaliel's Principle Trees On A Complex Plain Do Equal Bisectors Imply Isosceles? Continued Fractions and Characteristic Recurrences McCauley Cycles The Variance of Posterior Beliefs Collecting k Complete Sets of Coupons Double Equations from Triangles in Squares Global Reversibility of Cellular Automata Complete Solutions of Linear Systems Reflections on The Mirror Question Lorentz to Minkowski - Constructing the Principles More on Exhibited Conservation in QM Fiddling With Fibonacci One In The Chamber The Projection Postulate In Quantum Mechanics Kummer's Objection Omar Khayyam On Cubics Then There Were None Christmas Ornaments On a^4 + b^3 = c^2 Generating Random Numbers In Order On a Unit Fraction Question of Erdos and Graham Odd, Greedy, and Stubborn (Unit Fractions) Irrationality of Quadratic Sums The Phase Effect of Acceleration Tangent To PI Cyclic Redundancy Checks Average of Sigma(n)/n Rational Sines of Rational Multiples of PI The Super-Symmetric Mean The Ten Means of Ancient Greece Catch of the Day (153 Fishes) Generalized Eulerian Numbers Loxodromic Aliasing Carnot, Organizer of Transversals An Optical Illusion Frequency and Energy Weighing the Moon Logarithmic Integral and a Recurrence Newton And The Sun This Business of Interpretation Lucas's Primality Test With Factored N-1 Highly Heronian Ellipses Galois's Analysis of Analysis Reactionless Propulsion (Not) How Leibniz Might Have Anticipated Euler Wagon Trains and Sticky Wickets Factoring Zeta Some Properties of the Lucas Sequence (2,4,14,52,194,...) Four Squares From Three Numbers Ringing of the Changes (The Shape of 4!) Meandering Convergence of a Dirichlet Series Geodesic Diophantine Boxes Determining the Galois Group of a Polynomial Random Tiling of a Sphere Constructing the Heptadecagon Fourier Transforms and Uncertainty Least Significant Non-Zero Digit of n! Function 34776 Adam's Gold Zeno's Mice and the Logarithmic Spiral Unreasonable Effectiveness Relativistic Speed Composition Formulas Rigidly Re-Orienting An Extended Body Redundant Systems With A Common Threat Biased and Anti-Biased Variance Estimates Failure Rates, MTBFs, and All That Mean Partial Sums of Non-Convergent Series Formal-Numeric Series The Cube Unfolded Constant Headings and Rhumb Lines Markov's Marbles Enveloping Circular Arcs Normals From A Point To An Ellipse Discrete Fourier Transforms f(f(x))=exp(x) Generates the Multinomials Laplace Transforms Expulsion Sets Normal Shock Waves Discordance Impedes Square Magic No Four Rectangles In Line? Bi-Rational Substitutions Giving Squares A Plane-Tiling Triple Spiral Progress on Dedekind's Problem Expected Area of Random Polygon in a Circle The Tetratorus and Other Multi-Layered Polyhedra The Stars In The Sky Is e Normal? The Curvatures of Hypersurfaces Quantum Entanglement and Bell's Theorem The Thought of a Thought - Edgar Allan Poe Lagrangian and Hamiltonian Mechanics Time for a Rocking Chair Arranging the Solutions of f(x+y+z)=xyz Continuity and the Void Gerber's Gravity Does a Uniformly Accelerating Charge Radiate? From the Geometric Series to Stirling Numbers An Infinite Wall Platonions Conditions for Relativity Lorentz's Assumptions Potential Energy, Inertia, and Quantum Coherence Attractive Forces From Quantum Exchanges Coherent Arrays of Squares Zulu Hitler The Hydrogen Atom A Septagonal Non-Periodic Tiling Symmetric Pseudoprimes Linear Fractional Transformations Lead-Lag Algorithms Reflections on Relativity, Preface Experience and Spacetime Systems of Reference Inertia and Relativity The Dilemma of Light Corresponding States A More Practical Arrangement Staircase Wit Another Symmetry Generalized Lorentz Transformations Null Coordinates The Spacetime Interval Force Laws and Maxwell's Equations The Inertia of Energy Doppler Shift for Sound and Light Stellar Aberration Mobius Transformations of the Night Sky The Sagnac Effect Refraction Between Moving Media Accelerated Travels The Starry Messenger Thomas Precession Postulates and Principles Natural and Violent Motions De Mora Luminis Stationary Paths A Quintessence of So Subtle a Nature The End of My Latin Zeno and the Paradox of Motion A Very Beautiful Day Menelaus and Ceva Immovable Spacetime Inertial and Gravitational Separations Free-Fall Equations Force, Curvature, and Uncertainty Conventional Wisdom The Field of All Fields The Inertia of Twins The Breakdown of Simultaneity Absorbing Acceleration Tensors, Contravariant and Covariant Curvature, Intrinsic and Extrinsic Relatively Straight Schwarzschild Metric from Kepler's 3rd Law Curved Coordinates and Acceleration Riemannian Geometry The Field Equations An Exact Solution Anomalous Precession Bending Light Radial Paths in Spherically Symmetrical Fields Proper Time in Circular Orbits Flying Clocks Acceleration in Schwarzschild Coordinates Sources in Motion Is the Universe Closed? The Formation and Growth of Black Holes Falling Into and Hovering Near A Black Hole Curled-Up Dimensions Packing Universes In Spacetime Multiple Hubble Constants? Boundaries and Symmetries Global Interpretations of Local Experience Kepler, Napier, and the Third Law Newton's Cosmological Queries The Helen of Geometers Refractions On Relativity Scholium On Gauss' Mountains Strange Meeting Who Invented Relativity? Paths Not Taken In The Neighborhood Up To Diffeomorphism Higher-Order Metrics Spin and Polarization Entangled Events Von Neumann's Fifth Postulate Bell's Freedom The Gestalt of Determinism Imaginary Explanations Locality and Temporal Asymmetry Spacetime Mediation of Quantum Interactions Conclusion Mathematical Miscellany