## Elements of Geometry: A Brief Guide to the Euclidean Axioms

Euclidean geometry is based on Euclid’s axioms and postulates. What do the Euclidean axioms say, and why are they so important in math?

## Euclid Laid the Foundations of Geometry for Mathematics

Euclid’s geometry is still the cornerstone of today’s math theory, why are his axioms, theories, and postulates so important?

## T Cells, Predators and Finances all Walk the Levy Walk

University of Pennsylvania research shows that T cells “hunt” parasites in a “Lévy walk” pattern. This brings up a few questions for most of us, such as: Do T cells really walk? Who was Lévy, and … Just what is a “Lévy walk, anyway?”

## The Turing Machine versus the Decision Problem of Hilbert

David Hilbert raised the “Decision Problem,” or Entscheidungsproblem, in 1928. Turing Machines cannot solve Halting Problems, one specific type of decision problem.

## Algorithm to Solve Arranged Marriages via the Hall Theorem

According to Hall’s Marriage Theorem, a computer algorithm can correctly assign brides to grooms for optimum happiness. Dating services use computer programs to match prospective mates, but group matching by list is pure math theory.

## Is it Possible for Turing Machines to Solve the Halting Problem?

Alan Turing (1912-1954) “invented” his Turing Machine to represent the process of making mathematical inferences. The penultimate goal was to determine whether the “Halting Problem” could be solved. So, what’s the “Halting Problem?

## The Special Case of Non-Deterministic Turing Machines

Alan Turing (1912-1954) “invented” the Turing machine (TM) as a powerful theoretical model for mathematicians exploring rules-based mathematics. The  Non-deterministic Turing machine, or NTM, extends the basic concept by permitting multiple instructions for one state-input combination. The Deterministic Turing Machine A Turing machine has a finite number of states, symbols and instructions. A pattern of symbols are presented on […]

## Examples of Turing Machines: Loops, Halts, and Rewriting

A Turing machine, or TM, is a theoretical model devised by Alan Turing to explore the limits of rule-based math. The model has a finite number of rules, states and symbols, and an infinite tape with cells, each of which can contain a single symbol. The TM can either read the current cell, rewrite it, […]

## The Turing Machine: A Brief Introduction

Alan Turing (1912-1954) “invented” the Turing machine as a theoretical model for exploring the limits of rules-based mathematics. This purely theoretical device became a powerful tool in the minds of mathematicians, and modern computers still follow many of its principles. The Turing machine is even being honored via art at the Intuition and Ingenuity exhibit […]

## Potential New Algorithm to Calculate the Cube Root of a Number

Is there a new way to calculate a number’s cubed root? Recent news articles from India report that Mr. Nirbhay Singh Nahar has developed an algorithm to calculate the cube root of any number. Given an equation stating “y = x^3”, Nahar’s method would solve for “x = y^(1/3)” without the need to refine repeated […]