Famous Number Exercise, Statistics Problem Example

Activity
This activity will help you recognize the importance of some very famous numbers, as well as learn more about approximations.

Directions
Using the Internet, provide three approximations of the number according to the name that is provided below. Then follow any additional instructions that may accompany that name below.

• Pi (?)
  Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

One-hundred: 3.14

One Ten-thousandths: 3.14159

One One-hundred-millionth: 3.14159265

Provide a short definition of Pi.

Pi is referred to as the distance half-way around the edge of a circle, which is 3.14159265….

• Euler’s Constant (e)
  Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

One-hundred: 0.58

One Ten-thousandths:0.57722

One One-hundred-millionth: 0.577215665

Provide a short definition of e.

The Euler-Masheroni constant, also referred to as “Euller’s constrant” is the limit of the sequence Hn is a harmonic number, where

• Square Root of 2 (?2)
  Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

One-hundred: 1.42

One Ten-thousandths:1.41421

One One-hundred-millionth: 1.41421356

Provide a short description of why it is significant in history.

The square root of 2, most commonly referred to as (?2) is the positive algebraic number that gives the number 2 when multiplied by itself.  It also called the principle square root of 2. In addition, the square root of 2 is the length of a diagonal across of square of equal sides and is the first number known to be irrational.  Furthermore, this number was used in ancient mathematics and found on the Babylonian clay tablets and in ancient Indian mathematical texts.

• The Golden Ratio
  Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

One-hundred: 1.62

One Ten-thousandths:1.61803

One One-hundred-millionth: 1.61803399

Provide a short description of why it is significant in history.

The Golden Ratio was significant in history because during the 20^th century numerous artists and architects used the golden ration in their work.  They used this to form the golden rectangle since it was said to be aesthetically good for the human eye to view in that structure.