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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 leau
1910 - Girl with the Flaxen Hair 1918 - Death
Mona Lisa
Leonardo da Vinci
Early 1500s
Nicknamed for Leonardo da Pisa (1170-1250)
Fn+1 = Fn-1 + Fn , if n>1
F0 = 0 F1 = 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 = Ln-1 + Ln-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 leau 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.
Most lucid exposition of the structural and proportional
principles
Dramatic & Dynamic Shape
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
Paula A. Wilhite, Ed.D.
Northeast Texas Community College
A mathematician, like a painter or poet, is a maker of patterns. If his (her) patterns are more prominent than theirs, it is because they are made with ideas.