Learn from your mistakes

Right now in the year 2020, technology has advanced so much. We have smartphones, tablets and even lights that light up just by clapping your hands! Nowadays your smartphone can control your lights, TV. Even TVs have become super thin unlike the older bulky TVs. Technology has given us so many gadgets. Due to this our lives have become so easy with hardly any problems.

Replica of Thomas Edison's First Electric

However hundreds of years ago life wasn't the same. Life was extremely difficult. Communication was a task. Letters took a long time to deliver and the reply took even longer. During day people worked but during the evening they were dependend on candle lamps. There were many problems. But one scientist’s inventions changed the world. His name was Thomas Edison.

He was born in the USA and was known as America’s greatest inventor. Edison invented many things such as the gramophone, motion picture camera and his most important invention was the electric light bulb. Today let me tell you a story about how Edison invented the light bulb. He tried to used different materials for the filament to make the light bulb and he failed 2,000 times. All these materials failed to create the bulb.

Edison’s assistant said, “All our hard work is in vain. We wasted our time and have learned nothing. I am not sure if we will ever be successful in making the bulb." Edison replied very confidently, “I know we have failed 2,000 times. Now I have learned that these 2,000 materials can never be used to create the bulb.

Now I can try with other materials. Edison finally found the right material and created the light bulb! Thomas Edison's invention has changed the world forever!

Moral of the Story:

If you want to be successful, first learn from your mistakes. When you learn from your mistakes, you will not repeat them again. This help will you succeed. No matter how many times you fail, never give up! Keep learning and you will succeed!

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Connection Between Fibonacci Numbers and The Golden Ratio

Welcome. In this blog I will tell you relation between the Fibonacci Sequences and the Golden Ratio.Before that below you can see the statue of Fibonacci, made in 1863 by Giovanni Paganucci, a sculpture in florence, but kept in a ancient cemetery in pisa where the Fibonacci was born. Its is interesting that the likeness of Fibonacci in this statue and his iconic portrait probably looks nothing like Fibonacci, since no true drawings of him exist from 850 years ago . But nevertheless Italy still honors him with this sculpture. Statue Of Fibonacci Let's Return to Fibonacci Numbers and Fibonacci recursion relation. Then we will show you how they are related to Golden Ratio. So let's do some mathematics. Any way what's the recursion relation do you remember?? The n+1 Fibonacci number is equal to the sum of preceding two that is nth Fibonacci number Plus n-1 Fibonacci number right . Fn+1 = Fn + Fn−...

Fibonacci Sequence Problem set 1

Problems 1. The Fibonacci numbers can be extended to zero and negative indices using the relation Fn = Fn+2 − Fn+1 . Determine F0 and find a general formula for F−n in terms of Fn. Prove your result using mathematical induction. Solution: F0 = F2 − F1 = 0, F−1 = F1 − F0 = 1, F−2 = F0 − F−1 = −1, F−3 = F−1 − F−2 = 2, F−4 = F−2 − F−3 = −3, F−5 = F−3 − F−4 = 5, F−6 = F−4 − F−5 = −8. The correct relation appears to be F−n = (−1)^(n+1)×Fn .............(1) We now prove equation (1) by mathematical induction. Base case: Our calculation above already shows that equation (1) is true for n = 1 and n = 2, that is, F−1 = F1 and F−2 = −F2. Induction step: Let us assume that (1) is true for positive integers n = k − 1 and n = k. Then we have F−(k+1) = F−(k−1) − F(−k) ..(from definition) = (−1)^k×Fk−1 − (−1)^(k+1)×Fk ...

The Golden Ratio Divine Numbers By Luca Pacioli

Welcome. So below you can see very beautiful painting of Friar Luca Pacioli. Luca Pacioli was a religious man but he was also a Mathematician . And because of his standing as mathematician he became the teacher and good friend of Leonardo Da Vinci. Who is the most famous of all the renaissance men . Luca Pacioli Luca Pacioli is known as the Father of Accounting and Bookkeeping. But our interest in him is because he was the author of a book called the "De Divina Proportione" or "On the Divine proportion". The Divine proportion is a number . It's a number that we call now the Golden Ratio. Luca Pacioli thought this number was divine, was godly number. We are going to see that this number has a very close relationship with Fibonacci Sequence. What Is GOLDEN RATIO ?? We can understand what the Golden Ratio is by starting with a line segment and dividing the line segment into two segments. Lets Say one of length x and one of length y . Assuming that length x is lar...

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