Pythagoras Fundamental
Hi guys in this exam I am very excited we are going to start to see Pythagoras theorem
in picture form, in a very visual format.
So you can start to see what this all square stuff actual meaning.
So let us take a look at this a triangle we have here.
We have a black triangle is surrounded by all this grids as you can see.
The black triangle is a right angle triangle we know it is a right angle triangle because
it has a green thing here denoting and representing 90 degrees.
So as we look around we have these grids and we have the long hypotenuse here on that side
and the right angle over here as mentioned earlier.
So what we got to do is we play Pythagoras theorem in such a way that we can start to
see if it is false or true or not.
So first of all the best ways to play with this visually understand is to work with the
length of a black angle triangle.
So let us take a closer look at the length up here in orange, the length up here is 1,2,3
units so let us write that down 3 unit over there and the length across here is 1, 2,3,4
unit so let us write that down 4 over here and finally the hypotenuse the longer length
along here that is actually 5 units, 1,2,3,4,5, let us write down the 5 over here.
Ok let us see if we can do this in a short cut method and we can come up with a theorem
may be a little bit Pythagoras theorem.
Let us actually do this.
let us add the first two numbers the Y Pythagoras added the first two numbers let us see if
it is equals to the hypotenuse the last number on the right.
Ok we have 3+4=5, now thus 3+4=5?
No it does not?
Those it?
3+4 is 7.
So it does not =5, all they goes with that theory thus it not work too good?
Let us try and play now with Pythagoras theorem.
What he did is he square each number as you can see the each number is a squared, that
is a square, that is a square, the hypotenuse is also a square.
So let us square the number so let us take 3 and square it so we got 3squared and then
take the 4 and that is 4squared, take the 5 down here 5 by 5 that is 5squared.
Ok let us add the first 2 number and let see if it equals to the 3rd number.
Let us have a look how that works.
Now we have 3squared which is right over here, 3squared 3 equals 9, the 4squared that is
4 by 4 that = to 16 units squared, and finally we have 5 over here that is 5 by 5 that is
actually =25.
Let us see if the whole is true we have 9+16=25 let us see if the whole is true right now.
9+16 well that is 25, so we have here 25 equaling of course 25.
So is it not interesting?
When square each number it actually holds true so 25 thus not effect 25 by Pythagoras
theorem actually holds true now let us see how holds true visually up here displayed
in the picture , so we have a look here we have 9+16 equaling 25.
Well we have 9 here 3 by 3 is 9, we have 4 by 4 which is 16 over here.
Now we take the 9 and we added to the 16, 16+9 =25 it is the same number here 25 so
units clearly our right angle triangle, this 2 numbers when they are squared they equal
the hypotenuse squared.
so clearly by Pythagoras proof actually is true.
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