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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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