858 words - 3 pages

History of MathZeno of EleaZeno of Elea is a Greek mathematician. He would, however, be better described as aphilosopher. Little is known about his life for none of his own writings have survived. Most ofwhat is known about him comes from the writings of Aristotle. Zeno is said to have lived duringthe fifth century BC in the Greek town of Elea in southern Italy. Zeno is important to the study ofMath History because of his major contributions, the paradoxes, and some other minorcontributions.The most noted of Zeno's works are his paradoxes. Those dealing with plurality and withmotion. These were written in response to a theory circulating through the region concerning whatwe today would call a timespace continuum. The other Greek philosophers and mathematiciansthought that the world was a plurality of points and instants.1 This theory was started by thePathagoreans. They said the world had continuity. To contradict them, Zeno took their argumentsfor continuity to an extreme at which point they became absurd.To argue against plurality, Zeno said that if they are a continuous number of points thenthere is a given number of them. Yet, if they are finite, they cannot be infinite and plural. Thewhole point of his argument is to bring his opponents argument to a contradiction of logic. Thiswas a typical argument against plurality.Similar to Zeno's argument against plurality is his argument against motion. He did nottruly believe that motion, as given by the senses, exists. These paradoxes built around theargument of an infinite being finite make up the majority of his world view.The first paradox of motion is called the Dichotomy. It basically says that for an object totravel a given distance, it must first travel half that distance. A runner must run 1/2, then 1/4, then1/8, and so on ad infinitum. The runner must traverse each given distance in a given time interval,which is finite. The problem arises in that the runner must pass an infinite number of timeintervals to reach a finite goal.The second paradox is similar to the Dichotomy. The Achilles is a race between Achillesand a tortoise. The tortoise has been given a head start. Zeno says that Achilles will never passthe tortoise even though he runs faster. Achilles must first reach the tortoises starting point. Bythe time he does this, though, the tortoise has moved a distance. Achilles must then reach thatstarting point. This continues ad infinitum. Therefore, Achilles will never pass the tortoise and assuch lose the race.The third and fourth paradoxes take the opposite approach as the first two....

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