Elements of Geometry: A Brief Guide to the Euclidean Axioms

euclids geometry tools

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

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Euclid Laid the Foundations of Geometry for Mathematics

The Numbers of Euclid's Elements, image by Mike DeHaan

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

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The Turing Machine versus the Decision Problem of Hilbert

can a turing machine solve the halting problem

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

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Algorithm to Solve Arranged Marriages via the Hall Theorem

marriage via algorithm

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.

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

A Computer Magnetic Tape Drive is like a Turing Machine, by Steve Parker

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?

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