AMATYC 2013 Grand Salon E S063

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Paula A. Wilhite, Ed. D. Professor of Mathematics Division Director Math, Physics, & Engineering 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

Mona Lisa

Leonardo da Vinci

Early 1500s

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.

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

[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.