If you had been an average student like me during school/college days, then you would have definitely used bits in exam.
And there is a lot of techniques in that During my school days we used to write answers behind calculator or in small pieces of paper Kids nowadays use advanced technology to copy in exams One of the most important of it is micro Xerox The contents of 20 to 30 pages is reduced in size and printed in a single A4 paper and is used as a bit.
This is what a micro Xerox is If we don’t know proper mathematics while taking a micro Xerox, then we won’t be even able to prepare a bit “As we don’t know proper mathematics, we use bit in exams.
Do we need mathematics for this too? “ I can hear you people say that! Let’s see how to prepare bits effectively for exam using mathematics.
We use A4 size paper in our day to day life.
We use the same paper to take micro Xerox as well According to ISO 216 standards, the length of the paper is 297mm and breadth is 210mm you might wonder why they have chosen random numbers like this But there is a specialty behind these numbers If we divide the length by breadth, we will get 1.
414 We are familiar with this number! 1.
414 is the square root of 2 If we take an A4 sheet and tear it in half, we get two A5 sheet The length of this A5 sheet is 210mm and breadth is 148.
5mm If we divide the length by breadth, the ratio of this is also a square root of 2.
Likewise if you check the ratio of any A series paper, it will be a square root of 2.
For example, this is an A0 size paper.
If you check its ratio, it will be square root of 2 If we fold this paper in half we will get two A1 sheets If you check the ratio of this paper, it will also be a square root of 2 If we fold the A1 paper in half we will get A2 paper The ratio of this is also square root of 2 Is it not very surprising to see this? You might think is it necessary to maintain this square root of 2 ratio while manufacturing paper.
Yes! It is important.
if the papers are not designed in square root of 2ratio.
We won’t be able to prepare bit, Before that let’s see why A series papers are designed in square root of 2 ratio.
Let us consider this as an A4 paper I don’t know its length and breadth So, we can take ‘x’ as itslength and ‘y ‘as its breadth.
Now To prepare the next size paper from this, we will divide this in half.
Now, I will draw that here.
The length of this paper is ‘y’ and its breadth is ‘x/2’.
Our need to make sure that this paper’s length to breadth ratio should be equal to that paper’s length tobreadth ratio.
That is, the length of this paper is ‘x’ divided by its breadth ‘y’ is equal to the length of this paper ‘y’ divided by its breadth ‘x/2’.
To solve this formula, ‘x’ will go here and ‘y’ will go here.
so x(square) is equal to 2y(square).
To solve this further, x(square) by y(square) is equal to 2.
Now if we take square root on both the sides, square root of x(square) by y(square) will be equal tosquare root of 2.
So, x/y is equal to square root of 2.
so the ratio of any two paper has to be square root of 2.
When we manufacture a paper in this ratio, even if we fold the paper many times, the same ratio ismaintained.
Now we will see what happens when we design a paper taking random length and random breadth thatdoesn’t give square root of 2 ratio.
I have a paper of height 300mm and width 240mm.
we can consider this as an A4 sheet.
Half of this, that is, we will create an A5 sheet I will place the sheet I created here.
I will rotate this sheet vertically that it matches with the other sheet.
Now I will place the A4 sheet over A5 sheet.
I will now try to fix the content of A4 sheet in the A5 sheet.
If I match the height at the bottom, you can see that some of the data is lost at the side.
Again, if I try to match at the side, there is excess space at the bottom of A5 sheet.
We will have to face such problems if we don’t design our paper in square root of 2 ratio.
Now let’s take an A4 sheet which we use regularly.
If we look at its ratio, it is exactly square root of 2.
I will place one half of this, that is, A5 paper here.
Now I will try to fix the contents of A4 in A5.
You can see that it exactly fits inside So if we design a paper in square root of 2 ratio, we won’t lose any of our data When we try to micro Xerox in of any A series paper that has square root of two ratio, even the contentsin A4 paper will fit perfectly in A8 paper.
But if we try to micro Xerox in a paper with ratio not equal to square root of 2, we either tend to losedata or have excess space in our paper and the efficiency in our bit is lost.
I hope you have understood the relation between mathematics and preparing bit.
This doesn’t mean, wesupport you in copying.
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