## Thursday, February 7, 2013

### Bear Grylls and Pythagoras Theorem

Pythagoras is famous for proving that once you know the two sides of a right angle triangle you can work out the length of the 3rd side.
Pythagoras used fancy words like hypotenuse and mentioned squared numbers and roots a lot.
Pythagoras was indeed a very clever mathematician.

What does this all have to do with Bear Grylls and how does the theorem have any relevance to real life?

Below is a short example of how I taught my 13 year old son today. We were focusing on squared numbers (a number x by itself) and on squared roots (the number that can be multiplied by itself.)
For example 5 squared is 5x5 5x5=25 and the squared root of 25 is 5.

Scenario: You are Bear and you are in a hurry to escape the dangerous forest floor. The only suitable tree around is covered in slippery, wet moss and has no low limbs.
You need to climb this tree but don't want to risk scaling it and slipping. Thankfully you have your vine rope and a fallen tree nearby.

The ground near the tree is covered in tree roots and is very uneven. You will need to stand 30m away from it's base. The lowest branch is 50m up the tree. You measure your fallen tree and find it is 59m long. But is is enough?
To find out....
Square the distance from you to the tree (30m) 30sqd = 900
Square the distance from the base of the tree to the lowest branch (50m) 50sqd is 2500.
Add the 2 numbers together. 2500 +900 = 3400.
Find the square root 3400. Sq r of 3400 = 58.3
Your fallen tree is 59m, the length you need it to be is at least 58.3m so your trunk is long enough!

Pythagoras said the  2 known sides added together (3400) will be the same as the longest side squared (58.3 x 58.3) 58.3sqd  = 3398.  3398 rounded to the nearest whole number is 3400!

Personally, I am not keen on math and it's definitely not my strong point. What I do have is a strong interest in teaching my children and a strong belief that anything can be taught in a relevant and interesting way. When looking online for real life application of squared roots I found an example similar to mine but using a cat stuck up a flag pole. My son has aspergers and wasn't to fussed about the cat, making the cat/flag pole situation a bad example! Bear Grylls though is a hero and that's a different thing all together!

Total cost of this lesson: Nothing! Now that's thrifty :)