Structure of (a + b)^2
In our daily life mathematics plays an important role, which deserves much things to server, which is also know as mother of inventions. We all know the one great proved that is “Necessity is the mother of inventions” that’s why I said mathematics is necessity for creations. Mathematics which plays in all jobs and creations. Recently I studied a structure behind the mathematics, that concepts describe many things. We all know that the basic revert formula in mathematics that is which is my favourite formula also. But we didn’t know why the formula contains . One Basic thing was in Structural Mathematics, that is every formula represented in a way of shapes, so that contains either area or surface area. Now I used a same concept for playing with formulae.
Now in this week I plucked a two structural mathematics formulae, one is linear algebraic formula , next one is world’s famous and unbelievable first theorem, that is Pythagoras theorem . By using the structural mathematics, we have found some magic.
- Den algebraic formula of mathematics
I have already mentioned above all the mathematics formulae contain shapes, either that contains area or surface area. In here we considered an area construction for the above mentioned formula
Let us consider a two variable x, y, then consider an arbitrary line and arbitrary point,
Then our main goal is square of the (x + y). By structural mathematics that line shows “x + y”, Now I converted this line in to square, Let’s see
In above mentioned picture we can able to find the four sections, which can be divided from a one large single square. We know that the area of the square is squares of their length (If a = 5: there are is 25, unit depends upon the given criteria). Similarly, area of the rectangle is product of the length and breath of the rectangle (if length is l and breath is b, then the area of the rectangle is l x b). So, using these objectives we can able to verify that formula.
Now carefully read:
Now both the sides are verified, which is called as structural learning of mathematics.
- Pythagoras theorem
In here I did the same technique to predict the verification of the Pythagoras theorem by structural learning. Now I have a raised a question to myself (You have to raise to yourself, ask a question to yourself). What is Pythagoras theorem, all are said, Pythagoras theorem states that in a right angle triangle sum of the squares of the opposite side and adjacent side is equal to square of the hypotonus side when an angle α poses in a triangle. We all know that as an elementary study, but some real magic was there in this concept, that is structured learning. We all know that right angle triangle possesses an angle 90 degree, which triangle may be in three formats. Let’s see here.
In right angle triangle opposite side and adjacent side will vary for each condition, how the theorem works, how it verifies . Now we have to move the structural mathematics concept. Let us consider a two variable x, y, then consider an arbitrary line and arbitrary point.
Now the arbitrary line turns into the square. Which is similar to above mentioned example, but some simple modifications were there.
Joint the arbitrary points inside the large square which gives a sub — square in that square. By visibly large square contains one square and four right angle triangles. Same objective concept was applied here, area of the large square contains a length a + b is . Which may be equal to sum of the area of the four right angle triangle and area of the sub — square.
Let’s see their verification:
Thus, the theorem was verified. By using this structural learning mathematics, we can able to attain whatever the formulae such as matrices, differentiation and integration. Hope learning to create a creation like wise. Maths deserves so many things. We have to follow the Mathematics role, not in study role, we have to do in our daily life. I will be getting a hope to became best. So, you have to trust yourself to get some growth in your part of life.
