Four thousand years ago people discovered that the ratio of the circumference of a circle to its diameter was about 3. People saw circles in nature and realized that this ratio was an important tool. As mathematicians and scientists struggled to find a more accurate measurement of Pi, they found that Pi is an irrational number. This means that it can't be accurately represented as a fraction and that it continues indefinitely after the decimal place. However, there are some fractions (such as 22/7) that are close enough to do most calculations.
Click Here to view the first 1000 digits of Pi.
Over a century after the discovery made in
1766 by German mathematician and cartographer Lambert that Pi was
irrational, another German mathematician named Lindeman calculated that Pi was
also a transcendental number. A transcendental number is one which cannot
be the root of any algebraic equation with integer coefficients. The base
of the natural logarithm, known as e, is another number that has been
proved irrational and transcendental. Click
Here to learn more about e.
It is interesting to note that both these discoveries were made in Germany. Where have other discoveries about Pi been made? The map below illustrates the progression of discoveries about Pi throughout time. The findings about Pi began in Babylonia over 4,000 years ago and progress through a relatively small amount of countries. Think about what these countries had in common in order to connect their interest in mathematics and the number Pi. To further explore the mathematics that was occurring in these countries look at this MAP.
MMapping the Advancement of Pi
|Saudia Arabia/Iraq||Babylonians||~2000 B.C.||3.125|
|Israel/Egypt||Found in Old Testament||~550 B.C.||3|
|China||Chung Huing||~300 A.D.||sqrt(10)=3.16...|
|China||Wang Fau||263 A.D.||3.14|
|China||Tsu Chung-Chi||~500 A.D.||3.1415926<Pi<3.1415929|
|Germany||Ludolph van Ceulen||1596||Pi to 35 decimal places|
|England||Machin||1706||100 decimal places|
|Germany||Lambert||1766||Shows Pi is irrational|
|Germany||Richter||1855||500 decimal places|
|Germany||Lindeman||1882||Shows Pi is trascendental|
|England||Ferguson||1947||808 decimal places|
|USA||Pegasus Computer||1957||7,840 decimal places|
|USA||CDC 6600||1967||500,000 decimal places|
Discover Pi for yourself with this Activity
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