1. The Golden Ratio Art, Architecture, and Music Jonah Arnheim Advisor Mr. Richard Hollenbeck

2. Determining the Extent of the Golden Ratio The Parthenon The Great Pyramid of Khufu The Works of Claude Debussy Le Corbusier’s Le Modulor Salvador Dalí’s The Sacrament of the Last Supper

3. The Parthenon - Athens, Greece – 432 BCE

5. The Great Pyramid of Khufu – El Giza, Egypt – 2500s BCE

6. hs b Height (h): 481.4 ft Base: 755.79 ft Half base (b): 377.895 ft Slant (s): 612.0 ft (612.0 ft)/(377.895 ft) = 1.619

7. Bars 120-125 of Jardins sous la pluie – 1903 Works of Claude Debussy

8. Le Modulor – Le Corbusier – 1955

9. Le Modulor – Le Corbusier – 1955

10. The Sacrament of the Last Supper – Salvador Dalí – 1955

11. The Sacrament of the Last Supper – Salvador Dalí – 1955 A B X C A C B 1 1 36 y 108 y = AB = 1.618

12. The Works of Georges Seurat (1859–1891) C

13. C Der Kanal von Gravelines, Petit-Fort-Philippe

14. C Le jardinier 1882

15. C Woman with Umbrella – 1884

16. C Sitzender Mann – 1883

17. C Figures assises – 1883

18. C Sunday Afternoon on the Island of La Grande Jatte - 1886

19. C Luca Pacioli (1445–1517) and Leonardo Da Vinci (1452–1519)

20. C

21. C Polyhedra- Leonardo Da Vinci in collaboration with Luca Pacioli

22. C Mona Lisa- 1517 Leonardo Da Vinci

23. C Architecture

24. C Taj Mahal – Agra, India – 1648

25. C CN Tower – Toronto, Ontario, Canada – 1976

26. Notre-Dame – Paris, France – 1345

27. C Final Thoughts

28. C Questions

29. http://www2.ssso.southwark.sch.uk/page/?pid=228 http://nypost.com/2014/01/26/the-secret-history-of-the- parthenon/ http://egyptphoto.ncf.ca/pyramid%20of%20Khufu.htm http://drawingfor.wordpress.com/2012/01/26/anatomy- and-canone/45_le-corbusier-le-modulor-dor/ http://www.fondationlecorbusier.fr/corbuweb/morpheus.as px?sysId=13&IrisObjectId=6519&sysLanguage=fr- fr&itemPos=13&itemSort=fr- fr_sort_string1%20&itemCount=22&sysParentName=&sys ParentId=74 http://www.goldennumber.net/georges-seurat-golden-ratio- in-art/ http://en.wikipedia.org/wiki/File:Mona_Lisa_Golden_Ratio.jp g http://en.wikipedia.org/wiki/Polyhedron

30. http://en.wikipedia.org/wiki/Luca_Pacioli http://www.goldennumber.net/architecture/ https://culturaleducation.wordpress.com/category/imaginat ion/page/2/