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Math Ib Portfolio Essay

  • Submitted by: 893075006
  • on April 19, 2009
  • Category: Miscellaneous
  • Length: 290 words

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Below is an essay on "Math Ib Portfolio" from Anti Essays, your source for research papers, essays, and term paper examples.

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- an+1=0.

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