Unit 3
Modeling Random Motion
[埋込みオブジェクト:../media/FlashChap3.swf]
Sections:
3.5 - Measuring Average Distances
3.6 - Proving Average Squared Difference (Optional)
3.7 - The Wandering Ant on a Square Grid
What does "random'' mean? Think carefully before you answer! The definition may not be as obvious as you think.
The result of a coin flip is not random, because there are only
two possible outcomes. True or False?
The result of rolling a 6-sided die is not random, because there
are only six possible outcomes. True or False?
Whether I win the state Lottery or not is random, because there
are so many people playing the Lottery at the same time. True or False?
The weather is random, because so many conditions affect the weather
that we cannot predict it. True or False?
The main theme of this site is the study of how order grows out
of randomness. Every structure in your body grows and every process
in your body takes place in the presence of randomly-agitated molecules.
Yet instead of being torn apart by this randomness, we survive.
We even thrive on the randomness of nature. How can this
be? Before we can begin to answer this question, we must study randomness
itself, and details of the staggering, zigzag paths that atoms and
molecules execute all around us.
Can order grow out of randomness? Think about the following question:
Previous: 2.6 - Research Projects