Corralling ideas on optimization Lalu Simcik, PhD Cabrillo College AMATYC 2009 lsimcik.
AMATYC 2013 Grand Salon E S063
Transcript of AMATYC 2013 Grand Salon E S063
Paula A. Wilhite, Ed. D.
Professor of Mathematics
Division Director Math, Physics, & Engineering
AMATYC 2013
Grand Salon E
S063
1862 - Birth
1870 - Music Lessons
1872 - Paris Conservatory
1879 - First Compositions
1890s - Clair de lune
1905 - Reflet de l’eau
1910 - Girl with the Flaxen Hair
1918 - Death
Nicknamed for Leonardo da Pisa (1170-1250)
Fn+1
= Fn-1
+ Fn , if n>1
F0 = 0 F
1 = 1
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
2 3 1.5
3 5 1.66667
5 8 1.6
8 13 1.625
13 21 1.6153846
21 34 1.6190476
34 55 1.6176471
55 89 1.6181818
89 144 1.6179775
French Mathematician Edouard Lucas (1842-1891)
Ln = L
n-1 + L
n-2 for n>1
L0 = 2
L1 = 1
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, …
55 bars of introduction to the last
movement of La mer;
21 bars of introduction to ‘Rondes de
Printemps’ from the orchestral Images;
34 bars comprising the first
3/8 section of Jeux;
34 bars in first reprise of ‘Reflets dans l’eau’
55 bars to the beginning of its climax.
Three primary GS divisions
40 bars: 25 bars 16 bars: 10 bars
24 bars: 15 bars
All above equivalent to 8:5
8 and 5 are both Fibonacci numbers.
Total: 94 bars
Dynamic Focus: 58 bars
Overall GS -- 94:58
Cancels to 47:29 -- Lucas Numbers
Primary GS -- 34:21
Secondary GS -- 15:24
Cancels to 13:8 – Fibonacci Numbers
Overall GS 39: 23 bars
One bar removed from 13:8
GS of GS 26: 10 bars
Cancels to 13:5 – Fibonacci Numbers
Central GS 5: 3 bars
or 15:9 beats
Cancels to 5:3 – Fibonacci Numbers
Dr. Ron Clinton
Executive Vice President for Instruction
Mary Galloway Wade
Technical Designer
Mary Lou Goodson
Videographer
Crilly, David. Perception of Mathematical Structure and Architectural Design: Form and ‘Forming’ in Music. Department of Music, Anglia Polytechnic University, Cambridge, England. Griffiths, Paul. 1985. Modern Music, A Concise History from Debussy to Boulez. New York: Thames and Hudson Inc. Howat, Roy. 1983. Debussy in Proportion; A Musical Analysis. Great Britain: Cambridge University Press.
McHard, James L. 2008. The Future of Modern Music. Michigan: Iconic Press. Pages 45 – 53. Rosen, Kenneth H. 2000. Elementary Number Theory and Its Applications. 4th Edition. New York: Addison Wesley Longman, Inc. www.debussy.fr/encd/bio/bio1_62-82.php www.goldennumber.net/architecture/fineart www.maa.org/2008foundmath/2009foundmath www.maths.surrey.ac.uk/hostedsites