Math, Music and Identity

Homework Assignment #2

Due Friday, Feb. 27, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to A First Course in Math and Music, the primary text for the class (available on Moodle). You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Be sure to cite any references, websites, Internet sources, etc. that you may have used for assistance with the assignment.

Important: Please list the names of any students you worked with on the top of your assignment.

[I]t should be frankly admitted that in some plants the numbers do not belong to the sequence of f's [Fibonacci numbers] but to the sequence of g's [Lucas numbers] or even to the still more anomalous sequences

3, 1, 4, 5, 9, ... or 5, 2, 7, 9, 16, ... .

Thus we must face the fact that [Fibonacci] phyllotaxis is really not a universal law but only a fascinatingly prevalent tendency.

- H. S. M. Coxeter, from Introduction to Geometry (1961, Wiley, p. 172)

Section 5.2 (pages 190-191)
Problems:   2, 3, 4, 5

Note: For #2, don't worry about the last part of the question (the part about why you have to round off more with 150 than 144).

Additional problem: Please complete Exercise #5 on the Fibonacci numbers worksheet .