Once upon a time, there was a young athletic boy hungry for success for whom winning was everything and success was measured just by winning. One day, the boy was preparing himself for a running competition in his small village, himself and two other young boys to compete. A large crowd had gathered to witness the sporting spectacle and a wise old man, upon hearing of the little boy, had travelled far to bear witness also. The race commenced, looking like a level heat at the finishing line, but sure enough the boy dug deep and called on his determination, strength and power. He took the winning line and was first. The crowd was ecstatic and cheered and waved at the boy. The wise man remained still and calm expressing no sentiment. The little boy, however felt proud and important. A second race was called, and two new young fit, challenges came forward, to run with the little boy. The race was started and sure enough the little boy came through and finished first once again. The crowd was ecstatic again and cheered and waved at the boy. The wise man remained still and calm again expressing no sentiment. The little boy, however felt proud and important. “Another race, another race!” pleaded the little boy. The wise old man stepped forward and presented the little boy with two new challenges an elderly frail lady and a blind man. “What is this?”, quizzed the little boy. “This is no race” he exclaimed. “Race!”, said the wise man. The race was started and the boy was the only finisher, the other two challengers left standing at the starting line. The little boy was ecstatic, he raised his arms in delight. The crowd however were silent, showing no sentiment toward the little boy. “What has happened? Why not do the people join in my success?” he asked the wise old man. “Race again”, replied the wise man, “ this time, finish together, all three of you, finish together” continued the wise man. The little boy thought a little stood in the middle of the blind man and the frail old lady, and then look the two challengers by the hand. The race began and the little boy walked slowly, ever so slowly, to the finishing line and crossed it. The crowd were ecstatic and cheered and waved at the boy. The wise man smiled, gently nodding his head. The little boy felt proud and important. “old man, I understand not! Who are the crowd cheering for? Which one of us three?” asked the little boy. The wise old man looked into the little boy’s eyes, placing his hands on the boy’s shoulders, and replied softly.

 Have you ever wondered how pi was calculated before Newton
discovered it. Up until the 250BC, mathematicians knew for a fact that the
value of pi is between 3 and 4. And you may ask that how did they know that,
the answer to that would be that they did that with the help of a hexagon and
square.

A unit circle (area = π)
was inscribed with a regular hexagon of unit sides. And the circle was inscribed in a
square. The hexagon was then further divided into 6 equilateral triangles with
unit sides. Then the perimeter of hexagon was found to be 6 units. Since the
hexagon was inside the circle the circumference of the circle must be a little more than
that of hexagon.

Circumference > perimeter

2 π > 6

π >3

On the other hand, the perimeter of square > circumference of the
circle.

2 π<8

π <4

Hence, it was concluded to be between 3 and 4, i.e, 3< π<4.

Later in the 250BC, Archimedes improved this calculation. He bisected
the hexagon into a dodecagon (12 sides) and inscribed one into the circle and inscribed
the circle in another 12-sided polygon. After calculation, it was found that π
lies between 6.212 and 6.431. This process repeated for centuries until they
reached the 96-sided polygon and found a range of 3.1408< π<3.1429.

In the late 16^th century, Francois Viète
doubled a dozen times than Archimedes and computed the perimeters of polygon of
393,216 sides. And by the early 17^th century, Ludolph van Caulen surpassed
him by calculating perimeter of polygon of 2^62 sides. He spent 25 years of his
life calculating π upto 35 correct decimal places.

People were used this method of computing pi until Sir Newton came along.
The first step to his discovery of π was building Binomial theorem from the
Pascals triangle. Sooner after he also delt with the theorem being subjected to
incompetency when power of (1+x) was -1, since it would give an infinite
series. But he proved its accuracy by multiplying both sides by (1+x). The left
hand side gave 1 straightaway and when (1+x) was multiplied on the right hand
side, every term got cancelled leaving only one.

Afterward he went for (1+x) with power of ½ to solve for the area of a
unit circle by equation of the circle, which was given by x^2+y^2=1. Hence, the value y=(1-x^2)^1/2 can be calculated by substituting the value of x by -x^2.

Right after this, he also invented calculus. And the integration from 0 to 1
was used to find the area under y=(1-x^2)^1/2 which is the area of the quarter of
circle in the first quadrant. We also know that the area of quarter of circle
is (πr^2)/4. In this case it will be π/4 (since r=1). Upon equating them and calculating we get
the value of π. To make things easier and accurate he decided to integrate from
0 to ½. It gives the area of the circle from the left of y axis to the straight line of
x=1/2. That area can be calculated as area of a sector of 30 degrees, which
will be π/12, and a right triangle of sides 1 and ½ ( we can calculate the
third by Pythagoras).

And upon equating we once again can find the value of π. Not only that
but when you solve up to 5 places of the integration, you get results π for up to 5 decimal places. And it
will take calculation of integration up to 35 terms to get what Ludolph
van Caulen got after 25 years. This is how years of calculation was simplified
by Sir Isaac in a way it took only a few days to learn the value of pi.

SOURCE- Veritasium on youtube

The most important medium used in education today is the printed word. Knowledge is preserved in books and the first step in education is learning to read. But a blind man cannot read a book. is he then to be denied opportunities to educate himself? No, not necessarily so. The blind can get themselves educated, not only in the sense of being able to read and write but even in the sense of training themselves for the profession. Teachers of the blind have devised methods by which the blind can ‘read’ books without the aid of the eyes. The most famous of these methods is, undoubtedly, Braille.

Braille ( named after its inventor ) is a system of representation of printed symbols by raised dots on a flat surface. Six dots in various combinations are used to represent letters, numbers, punctuation marks, and some common words. The blind person ‘reads’ the boo by passing his fingers over the dots. Thousands of blind people all over the world have used Braille to educate themselves. A book in Braille is not so compact or handy as compared to any other book. The size makes it difficult for people to use Braille as easily as printed books.

To overcome the difficulties, a new method has been introduced in recent times. The American Association for the Blind made ‘Talking books’ or long-playing discs with recordings of books. The popularity of talking books and tape recording is steadily increasing, and governments and private agencies have come forward to support the effort to produce them and make them available to people who need them.