As a math teacher, I spend a lot of time thinking and talking about numbers. As math students, I would suggest you also spend a lot of time thinking and talking about numbers.
There’s one group of numbers that I find very interesting. They are kind of the odd balls of the number system - irrational numbers.
First - what is an irrational number?
Let’s think about the word “irrational” for a moment. According to Thesauraus.com, synonyms for irrational include unreasonable, illogical, unjustifiable and more.
To put it simply, irrationals are the crazy numbers.
An irrational number looks like any other fraction - for example: 22/7 - but there’s a catch. You can write 22/7 as a decimal and it looks like 3.14285714 and the decimal places go on forever, never repeats and never ends. (You might recognize that number as Pi - an important number in math circles.)
And here’s the part of that crazy that boggles my mind: You can never get an exact answer.
Think about it - If I ask you to calculate the ratio of a circle’s circumference and diameter you’re going to tell me it’s 3.14 or Pi. But that’s not really true. It’s more of an approximation. Because the number changes depending on how many decimal places we look at.
3.14 is not the same as 3.1415. They are different numbers and, yet, we accept both as being equal to Pi. We have to accept that the value we place on any irrational number is not exact, and it can’t ever be exact, because the decimals go on forever.
It’s irrational to think like that but we do.
100 Posts!
ReplyDeleteI think if you are going to call the irrational numbers the odd balls of the number system, you must first consider the complex numbers. Taking the square root of a negative number is more mind-blowing than even irrationals, though I do agree that irrationals are very weird.
ReplyDelete-RM, McKellar Crew