The Mathophile

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Power of Mathematics || Small story #006

There was a big empire of king Ramulo somewhere in the middle of Asia. He was the most powerful king in whole continent. Also, he was wealthiest king of all the kings and people in his country where happy and everyone was rich enough. Nobody was poor and beggar there. And obviously the king also proud of this. But, eventually he was becoming arrogant and egoistic on his wealth and Empire as a king. Likewise the people in his Empire where following the same. The king Ramola had a daughter named Jasmine . She was very charming and beautiful. One day, Jasmine was wondering in the small village nearby. Suddenly she was caught by some soldiers of king's enemy's army. The brave and intelligent man named Akira saved Jasmine from enemies using his brain and took her to the king. king was worried about his daughter. As he saw her daughter he became very happy. He was impressed by Akira . He appealed Akira to ask for anything he want.

Ramanujan's Summation || What is the sum of all counting numbers?

Well, we all know that the sum of first n natural numbers is n(n+1)/2. Fine! But the mystery is, what is the sum of all counting numbers? Well, this is no longer a mystery, as the great Indian mathematician Srinivasa Ramanujan gave the sum for the same. Srinivasa Ramanujan He suggested that the sum of all counting numbers (all natural numbers upto ♾️) i.e. 1+2+3+4+5+6+7+ ••• upto ♾️ is -1/12. If you still feel it difficult to believe, if you think, how all positive numbers sum up to negative number? Well, don't think too much, keep reading my article to unreveal all the mysteries. The following two series are the backbone of our proof for the sum: 1-1+1-1+1-1+1-1+1-1+ •••• = 1/2 1-2+3-4+5-6+7-8+9-10+ ••• = 1/4 Well we have already discussed about the first series, that is Grandi's series . The crazy one! In fact I have one whole article on this little beauty called Grandi's

Grandi's series

Grand's Series: Look at the following series, S = 1 − 1 + 1 − 1 + ⋯ which can be also represented as is called as Grandi's Series . The question that came to the ancient mathematician was, what is the sum of the series? Well, these mathematician came up with the two approaches as follows: 1 . They attack on the series like, (1 − 1) + (1 − 1) + (1 − 1) + ... = 0 + 0 + 0 + ... = 0. 2 . On the other hand some treat it like, 1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + ... = 1 + 0 + 0 + 0 + ... = 1. Well, both the results were very contradictory. By treating the above series in two different ways, one can get either 0 or 1 as an answer. In 1703, one Italian mathematician named Guido Grandi came up with the idea that the sum of above series is neither 0 nor 1, but it is 1/2 . After which many mathematician of the time disagreed and said, "what? The sum can't be 1/2." This was very hot topic for the debate in the mathematician of that time for some years. After s

Is Mathematics Discovered or Invented?

Would Mathematics exist if people didn't? In ancient time mankind had hotly debated whether mathematics was discovered or invented? Is it a product of human mind or it exist in realm? Did we purposely created it to understand the physical world around us or is it the intrinsic language of the universe itself ? And many such questions are always the hot topics to discuss about. We know mathematics has mysterious power to describe the patterns and The structures of the physical world. But have you ever tried to explore that. Lets for it right now. Now have a look at the following statements: 1 . There are 8 planets in our solar system. 2 . There are 1,14,353 trees in the forest. What do you think, does the existence of human affect the number of planets in our solar system or the number of trees in the forest. No. It doesn't . Weather human exist or not the number of trees and the planets are going to be same. But the poi

what is mathematics?

Hey guys, I am back with the very interesting topic. Most of you are from science and mathematics background. At Least you have studied Mathematics till 10th standard. So, have you ever try to explore “what is Mathematics?If you do, it’s fine. If not, let’s do it right now. Now, we will start from the ancient time of Pythagoras . So, question is what Mathematics was for those of Pythagoras and the people of that time. Why they use Mathematics ? What was the purpose? Now, have a look at the very basic theorem called Pythagoras Theorem: Pythagoras Theorem: a^2 + b^2 = c^2 for the following right angled triangle. What Pythagoras thereom explains is following: If you have two squares with areas 4 sq.units and 3 sq.units. when you add them together then the total area is going to be equivalent to the square with area 5 sq.units. That's it. Ancient people used to use mathematics in their daily life. If one person have 1

Katherine Johnson

KATHERINE JOHNSON Katherine Coleman Goble Johnson (born on 26 August 1918, Hampton- Virginia ) is an American mathematician who is well known for her mathematical calculations in orbital mechanics. The space agency noted her " historical role as one of the first African-American women to work as a NASA scientist ". Her contribution FOR NASA : Johnson's work included calculating trajectories, launch windows and emergency return paths for Project Mercury spaceflights . Katherine has referred to the women in the pool as virtual "computers who wore skirts".She spread her wisdom with her calculations in the trajectory for Project Mercury and Apollo 11 flight to the moon. She was an extraordinary woman with incredible talents. Career : Johnson showed strong mathematical abilities from an early age . After graduating from high school at 14, Johnson entered West Virginia State, a historically black college. Awards : Johnson won ma