# irrational

## Irrationality by Infinite Descent

The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the...

## Dedekind Cuts of Rational Numbers

Given a number line with equally spaced tick marks one unit apart, we know how to measure rational lengths: the...

## Computability of Real Numbers

We can write a computer program that will successively print out the digits of the decimal expansion of Pi. We...

## Rationals Dense but Sparse

Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the...

## Rational Irrational Power

If you raise an irrational number to a rational power, it is possible to get something rational. For instance, raise Sqrt to...

## Square Root of Two is Irrational

An irrational number is a number that cannot be expressed as a fraction. But are there any irrational numbers? It was known to...

## Fourier Ears Only

Did you know that every sufficiently smooth function on an interval can be expressed as an infinite sum of sines...

## Pi Approximations

Pi is the ratio of the circumference of a circle to its diameter. It is known to be irrational and its decimal...