«Αριθμός, το Πάν»
Lambert's W Function, Infinite Exponentials, Powertowers, Iterated Exponentials and Tetration (Preliminary results, 10 years ago. For published versions of the majority of this section, consult Google scholar [). 3]
A Strange Encounter With Johann Heinrich Lambert.
A Slightly Deeper Analysis of Infinite Exponentials.
A Maclaurin Expansion For Lambert's W function.
Approximating the Principal Branch of the Complex Lambert's W Function.
Approximating the Branches of the Complex Lambert's W Function Using Analytic Continuation.
An Infinite Family of Hyper-Lambert Functions and Their Use In Solving Exponential Tower Equations.
A Detailed Look at the Hyperroot Functions Using Lambert's W Function.
A Continuous Extension of the hyper4 Operator.
An Infinitely Differentiable Extension of the hyper4 Operator.
A Series Expansion of . m(e x) Using Lambert's W Function
A More Consistent Definition of Tetration For Rational Exponents.
The General Infinite Exponential and Its Limit.
The Analytic Continuation of the Infinite Hyperpower Function F(x) = . +∞x
The Infinite Tetration Fractal.
The Exponential Fractal.
A Strange Hyperexponential Series.
Solving the First Auxiliary Real Exponential Equation Using Lambert's W Function.
Solving the Second Auxiliary Real Exponential Equation Using Lambert's W Function.
Solving the n-th Auxiliary Real Exponential Equation.
A Family of Hyperpower/Hyperfactorial Series.
File Signatures and Tetration of 2.
A Collection of References For Infinite Exponentials and Tetration.
An Interesting Sequence of Cyclic Digits.
The 3n+1 problem.
Does Arc Light Flickering Interfere With Video?
Trends In Euler's Totient φ Function.
A Short Tutorial On Big Numbers.
The TetraMag Puzzle.
Harmonic Analysis, Fourier Analysis, Spectral Theory
Google Scholar and the Spectra of the Scientists.
Web Site Performance.
Suprema and Infima In Real Life.
The Cantor Function.
Temperatures On the Surface of the Earth.
Is There a Limit On How Fast the Olympic 100 Meters Can Be Ran?
Modelling Time Under Total Anesthesia.
An Infinite Hierarchy of Hyperfactorial Functions.
Overall Function Behavior.
Modelling Relative Mind Power Using the ELO Rating System. Combinatorics
A Program To Solve Loyd's Wooden Tile Puzzle.
A Program to (almost) Solve the 24, 3-color Tile Puzzle.
Distinct Resistances Possible With At Most n Distinct Resistors.
Find the Number! Topology
The Author's View of the Universe.
Philosophy of Mathematics
Can Mathematics Explain What Is Real?
Understanding Symbolic Levels.
Is The Mind Infinite?
The Importance of the Golden Ratio.
A Most Beautiful Construction In Mathematics.
How Fast Can You Count?
Is There a Veblen Hierarchy of Functions that Doesn't Cause an Untimely Collapse?
Estimating the Area and Perimeter of a Circle and π Using Archimedes' Method.
The Golden Ratio and Other Metal Ratios.
The Author's Webpage Statistics Projector.
Complex Analysis, Dynamical Systems and Fractals
Using Maple To Visualize the Complex w-Plane.
A Quick Comparison Between the Power Tower and the Mandelbrot Fractals.
The Mathematics of Chess
Every Chess Configuration.
The Main Principles of a Chess Engine.
The Attack-Force Metric In Chess.
Computer Science and Cryptography
How Does tinyurl Work?
The Dynamics of Computer Programming.
A Lossy Compression Scheme and Lossless Data Transmission.
An Application of Numerical Analysis To Science Fiction.
From Mathematics To Color Perception.
"The Problem of the Crack in the 'Generally' Anisotropic Disk" (English Translation of the author's
father's Ph.D. Thesis. Original Greek Title: "Το Πρόβλημα της Ρωγμής εις τον «Γενικώς» Ανισότροπον Δίσκον"). "The Problem of the Infinite Exponential", thesis submitted to the Mathematics Department of the Agricultural University of Athens.
, English . Greek Companion Maple code for some of the various exponential fractals of the thesis above, at:
Maple Primes. Notes
Function/data graphs done with
Maple and THINK Pascal and geometrical schematics with EucliDraw. Using LaTeX.