By Khinchin A.
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Additional info for A course of mathematical analysis
You will start seeing patterns after roughly 24 hours. The pattern will continue forming for about one and a half weeks to two weeks. Chapter 1. From Coin Flipping to Motion of Molecules 47 REFERENCE: This version of the Liesegang experiment was adapted from J. E. Forman, Journal of Chemical Education, Vol. 67, page 720, 1990 Contents Chapter 2. Fractals in Nature. 2. 6. 3. 4. 5. 6. 7. 11. Research! 21 Research on Electrochemical Deposition Research on Viscous Fingering Research on Bacterial Colonits Research on Termite Colonies Research on Roots Appendix A.
On the following two pages are several pictures of scraggly structures. What do they have in common? Answer the following questions and be prepared to discuss them. How are these objects similar to each other in appearance? In what ways do these objects look different? (1) (2) There are many ways to rank objects. For example, you can rank different students according to weight. You can also rank the same group of students by height or shoe size or age or hair color. Look at the photographs above and figure out different ways to rank these images.
After n steps we determine how far we are from the lamp post. , multiply it by itself) to get (~? [Why do we square it? ] Then we start again and take the same number, n steps, find a second value for xn and square it to get a second value for (x n )2. Do this again and 45 Chapter 1. From Coin Flipping to Motion of Molecules again. Finally average all the values we have obtained for (xn)2. Using carot brackets <> as a symbol for "average," we are finding the value of «xn )2>. 2 What do we expect the value of «x n ) > to be?
A course of mathematical analysis by Khinchin A.