Of Not Missing The Point

In every subject, I think it is very important to catch the main point. When we start school, generally, cause of our teachers’ deficiencies or laziness, we are always ‘told’ something again and again but indeed not taught really. Yeah, there are really good teachers but they are always outnumbered. Because of that, we always make films and TV series about them.

Catching the main point is the key…

Let’s give an example about this;

We all know the equation; $a^{2}+b^{2}=c^{2}$

We’re always said that this equation can be used when there is a triangle one of its angles is $90^o$ . The end! In this point, we’ve lost the point and a great good.

In reality, this pythagorean theorem can be used with any shape and for any formula that squares a number. Surprising, huh?

The area of any shape can bu computed from any line segment squared. Say a square (side 5, square 25) or a circle (radius 5, area 25* $\pi$ )

$Area=Factor*(linesegment)^{2}$ .

It can be a square, a rectangle, a triangle etc…

With same logic, this formula can be applied to any similar shape. All squares are similar ( $s^{2}$ ), same as all circles and same type of triangles.

Now, we may say;

Circle of radius 13 = circle of radius 5 + circle of radius 12 (Looks like 5-12-13 combination, huh?)

$13^{2}*\pi=5^{2}*\pi+12^{2}*\pi$

You may say, yeah it makes sense but it is still about geometry. What else?

Here it comes.

You know bubble-sort algorithm right? Its complexity is $n^{2}$ when there is $n$ input.

Using this equation, you can say;

50 inputs = 40 inputs + 30 inputs

which means 70 elements spread among two groups can be sorted as fast as 50 items in one group. (Yeah, there may be constant overhead/start up time).

Given this relationship, it makes sense to partition elements into separate groups and then sort the subgroups like quicksort. The Pythagorean theorem helps show how sorting 50 combined elements can be as slow as sorting 30 and 40 separate ones.

Interesting?

Inspired by [1]’s related post. With help of [2]
—

[1] : http://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/
[2] : http://en.wikipedia.org/wiki/Pythagorean_theorem

Share and Enjoy: