# Mathematics

## Modern Pythagorean Explanation

Pythago-Rock And Roll! Pythagoras probably never expected his theorem to be used to carry out the successful reunion tour for a relic from the grand old 1980’s. In this paper, I’ll be demonstrating how Pythagoras’ proof can be used to…

## How to use an Abacus

Calculators have only recently gained widespread popularity for their help in solving arithmetic problems which might be too difficult to figure out mentally. Even paper, pens and pencils are a luxury that we have only been able to enjoy relatively…

## The Difference between Independent and Dependent Variables

Many times, one hears about a recently published story that links soda consumption to obesity or smoking to lung disease. There are many more examples that one can find announced in a major newspaper, a popular magazine, a journal, or…

## Pi

The mathematical constant Pi occurs widely in mathematics and science. The number expresses the ratio of any circle’s circumference to its diameter. It also appears in higher level mathematics. For practical purposes there are two equations that regularly crop up…

## Zero

The Idea of Zero Mankind’s unrelenting search for knowledge has led to ideas that we find fundamental to modern thought. Such ideas, though commonplace and often regarded to be but simple concepts, are astoundingly deeply rooted in philosophical thought. The…

## Using Practical and Statistical Significance in Testing the Null Hypothesis

Statistical methods used to test the null hypothesis are commonly called tests of statistical significance. What happens is that researchers have the propensity to make statements in this regard: “The difference between the experimental and control group was significant at…

## Bayes Theorem Bayesian Statistics

Suppose you’re given a test to determine whether or not you have a rare, incurable, fatal disease. If you do, there’s a 99% chance that the test will be positive, but if you don’t there’s a 99% chance the test…

## Overview of Chemical Thermodynamics

Thermodynamics is a science which is built upon experimental facts that cannot be proven.  But no one has so far succeeded to refute these principles.  There are two experimental facts upon which thermodynamics is built.  These are: the law of…

## Counterexamples in Abstract Mathematics

When studying abstract mathematics, one of the best ways to understand the subtleties that are inherent in the abstraction is to keep certain illustrative examples in mind. This allows us to encode the properties of the math we are studying…

## Division zero Math Mathematics Abstract Idea – Yes

Consider Zero, if you will. What is zero if not an abstract idea, an elusive concept that you cannot see, nor hear, and certainly not touch, taste or smell. It is the stuff of dreams and nightmares. Imagine falling endlessly…