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Pi
1 students

Pi

Interesting and Useful Properties of Pi
Created byDavid Terr
Last updated 6/2024
English

What you'll learn

  • Learn the definition of pi and why it is important in math, science, and engineering.
  • Learn some fascinating mathematical properties of pi.
  • Learn various methods mathematicians have used to calculate pi.
  • Learn various ways pi has influenced our culture, including its use in the arts.

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Course content

1 section • 5 lectures • 1h 57m total length

  • Definition and Basic Properties28:26
  • Methods of Approximation25:43

    In this lesson, I discuss a host of methods that have been used to estimate pi, starting with Archimedes' method of exhaustion and ending with Chudnowski's infinite series formula, the fastest known converging series for pi. I also discuss the history of the number of known digits of pi, which is now over 100 trillion.

  • Pi in Advanced Math18:58

    In this lesson, I mention some areas of advanced mathematics that use pi, although none of these applications have any obvious connection with circles. These include the formula for the standard normal distribution discovered by Gauss in the early 19th century, and sums of reciprocals of even powers of positive integers (i.e., values of the Riemann zeta function evaluated at positive even integers.

  • PI in Science and Engineering26:00

    In this lesson, I describe some scientific theories and engineering applications that use formulas involving pi, and how they are used.

  • Pi in Art and Culture18:35

    In this final lesson, I discuss some purely aesthetic applications of pi, such as in architecture, art, music, literature, and humor.

Requirements

  • Students should have a good working knowledge of arithmetic as well as high school algebra and trigonometry.

Description

In this course, I discuss many interesting and important properties of pi, one of the most well-known concepts in mathematics.

In hte first video, I discuss some interesting and important mathematical properties of pi, starting with its definition and leading up to other mathematical equations involving pi, such as formulas for areas and volumes of circles, spheres, and hyperspheres of arbitrary dimensions.

In the second video, I discuss various methods that mathematicians have used to estimate the value of pi, starting with the method of exhaustion used by Archimedes and finishing with some rapidly converging infinite series formulas, the fastest of which has allowed for pi to be calculated to 100 trillion decimal places.

In the third video, I discuss how pi has been used in various areas of advanced mathematics where you might not expect to see it, such as the distribution of prime numbers as well as the formula for the normal distribution, which is widely used in statistics.

In the fourth video, I discuss how pi appears in many scientific formulas and thus is important in various areas of science and engineering.

In the fifth video, I discuss how pi has inspired various forms of creativity in our culture, including art, music, literature, and humor.

Who this course is for:

  • This course is intended for anyone who wants to learn math.

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