Math Ib Portfolio Essay

290 WordsApr 19, 20092 Pages
Surds are used commonly in math, they just are not referred to as surds. A surd is any positive number that is in square root form. Once you simplify the surd it must form a positive irrational number. If a natural number is formed, it is not considered to be a surd. Infinite surds are just surds forming a sequence that goes on forever. The exact value of an infinite surd is expressed in the square root form. When the infinite surds in those sequences are simplified, a never ending sequence of irrational numbers are revealed. The following is an the first example of an infinite surd: You may be wondering why this can be classified as a surd when is not a surd. simplified forms natural number and cannot be classified as a surd. As you can see in the first 10 terms of the infinite surd, they are all irrational numbers. a1: = 1.41421 ... a2: = 1.55377 ... a3: = 1.59805 ... a4: = 1.61184 ... a5: = 1.61612 ... a6: = 1.61744 ... a7: = 1.61785 ... a8: = 1.61797 ... a9: = 1.61801 ... a10: = 1.61802 ... From the first ten terms of the sequence you can see that the next sequence is the previous term. Turning that into a formula for an+1 in terms of an makes: From the plotted points of the infinite surd in graph 1, you can see that the more n increases, the closer an gets to the value of about 1.6181 but never touches it. This shows that the rise of the slope is getting increasingly smaller, so as n gets very large, an- an+1 gets closer to 0. Since the sequence goes on forever, it cannot be determined if an-

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