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

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

The Parthenon - Athens, Greece – 432 BCE

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

hs b Height (h): ft Base: ft Half base (b): ft Slant (s): ft (612.0 ft)/( ft) = 1.619

Bars of Jardins sous la pluie – 1903 Works of Claude Debussy

Le Modulor – Le Corbusier – 1955

Le Modulor – Le Corbusier – 1955

The Sacrament of the Last Supper – Salvador Dalí – 1955

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

The Works of Georges Seurat (1859–1891) C

C Der Kanal von Gravelines, Petit-Fort-Philippe

C Le jardinier 1882

C Woman with Umbrella – 1884

C Sitzender Mann – 1883

C Figures assises – 1883

C Sunday Afternoon on the Island of La Grande Jatte

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

C

C Polyhedra- Leonardo Da Vinci in collaboration with Luca Pacioli

C Mona Lisa Leonardo Da Vinci

C Architecture

C Taj Mahal – Agra, India – 1648

C CN Tower – Toronto, Ontario, Canada – 1976

Notre-Dame – Paris, France – 1345

C Final Thoughts

C Questions

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