MATH 265 DeVry University Number Pi in Mathematics Discussion Questions

Question Description

Let’s figure out what pi(π) equals. Most people know it’s approximately 3.14, but what if we wanted to know it more and more accurately? Here is a method to do so. From trigonometry, we know that

LaTeX: tan^{-1}left(1right)=frac{pi}{4}:

Use the series expansion for LaTeX: tan^{-1}left(xright):(from a table), substitute x=1 into the series and multiply all terms by 4 to have a series for π. Note that this series converges extremely slowly.

Determine π using…

  • the first term only
  • the first five terms
  • the first ten terms
  • the first fifteen terms

Do some research on π. Why is it such an important number? Who first discovered it and how? What is the longest known representation, in terms of digits? Do the digits repeat in any way? Is there a pattern in the digits that anyone has discovered?

Prof. Angela


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