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
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 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.
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.
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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
[email protected]
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.
