Wednesday, March 13, 2013

Completely Irrational

Happy Pi Day!

Pi is probably the most well known of all irrational numbers. Since it begins with 3.14, March 14th (3-14) is often referred to as pi day.

For those that are not into mathematics (rational or irrational), an irrational number cannot be expressed as a ratio of numbers.
For example:
2 can be expressed as 2/1 and is a rational number.
4.5 can be expressed as 9/2 and is a rational number.
Even .33333333... (3 repeating) can be expressed as 1/3 and is a rational number.

Irrational numbers never repeat as a decimal number and cannot be expressed as a fraction (a ratio of numbers).

From one site on irrational numbers comes this story:

History of Irrational Numbers

Apparently, Hippasus (one of Pythagoras' students) discovered irrational numbers when trying to represent the square root of 2 as a fraction (using geometry, it is thought). Instead he proved you couldn't write the square root of 2 as a fraction and so it was irrational.

However, Pythagoras could not accept the existence of irrational numbers, because he believed that all numbers had perfect values. But he could not disprove Hippasus' "irrational numbers" and so Hippasus was thrown overboard and drowned!

And I thought I had some tough teachers!

John <><


Mike said...

I always thought the sq rt of 2 was 1.4141414.... It's not. But that number is out there on the net. So other people think that also.

Remember "The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1"? That's where I remember that from. High school.

eViL pOp TaRt said...

It pays never to contradict teachers' pet theories, I learned at an early age.

Bilbo said...

A sound understanding of irrational numbers is essential to being able to follow discussions of fiscal matters in Congress and on shout radio.