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The history of the concept of limit Essay Example

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The history of the concept of limit

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He suspected the craftsmen used or mixed cheaper metals during its crafting to cut costs, yet he had no way of proving this was the case.In response to his personal query, he offered a reward to anyone who could solve this conundrum. Archimedes dared to take on this crowning dilemma. The legend has it; he solved the puzzle when he was bathing. While in the tub, he noticed, as he stepped into it, the levels of water on the side of the tub rose as he stepped in and resided and he stepped out.He connected the submersion of his body with mass and spacial displacement. He then realized that the mass of objects and the displacement of water when they were submerged was the key to solving the crown problem.Upon striking upon this notion, It is said, Archimedes leaped from the tub in excitement and raced naked trough the streets of Athens, shouting eureka (the Greek word for I found it) all the way to the Kings Court. This instance, perhaps, launched Archimedes study in area, which lead to the knowledge we have today in the concept of limit.One of the concepts Archimedes was interested in was finding the value of the diameter and volume of a circle. It was during this research, he founded . (In numeral terms 3.14) This symbol is as recognizable in mathematics as the sun is in the sky. This number is special in the fact that the decimal places never end.During his spherical research, he split up the sphere into several slices, which he attempted to find the area of. It was during his efforts in finding ; he started work of the measurements of parabolas.During this study and slicing, he proved the area of a parabola is four thirds the area of a triangle inside out. He computed the area of the parabola by enclosing a curved figure within a bigger one with straight edges. He then took the splices of empty space and measured the volume of each, using the concept of actual infinity.Sadly, several centuries later, after the fall of Rome, Math and science fell into a dark age. No new concepts were discovered outside of Arabia and China and many important works were either lost or destroyed. Fortunately, certain monasteries copied the old texts. These texts were discovered by later generations, sparking a Ressaisance in thought and discovery.During this process, these men started pondered on the concept of limit and started to seriously study it. Men who contributed to this study include: Isaac Barrow, Pierre de

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