CHAPTER-1-MMW2

• Golden ratio in arts

  • Phidias - Parthenon
  • Plato - Platonic solids
  • Leonardo di Ser Piero da Vinci - Mona Lisa
  • Michelangelo di Lodovico Buonarroti Simon - The Creation of Adam
  • Raffaello Sanzio da Urbino - The School of Athens
  • Alessandro di Mariano di Vanni Filipepi - The Birth of Venus
  • Georges-Pierre Seurat - Bathers at Asnieres
  • Salvador Domingo Felipe Jacinto Dalí - The Sacrament of the Last Supper
• Pattern in nature


  Visible regularities of form found in the natural world and can also be seen in the universe, modelled mathematically, can be observed even in the stars, can be seen in fish patterns
• Fibonacci sequence


  The sequence of numbers in which each number in the sequence is equal to the sum of two numbers before it
• Fibonacci spirals


  • Pine cones
  • Pineapples
• Golden ratio


  A relationship between numbers on the Fibonacci sequence where plotting the relationship on scales results in spiral shape, the most important part of human beauty and aesthetics as well as a part of the remarkable proportions
• Golden ratio in nature


  • Fern fiddleheads
  • Flower buds
  • Spirals in shells
  • Spirals on human face
• Golden ratio in arts

  • Phidias
  • Plato
  • Euclid
  • Leonardo di ser piero da vinci
  • Michelangelo di lodovico simon
  • Raffaello sanzio da urbino
  • Alessandro di mariano di vanni felipepi
  • George-pierre seurat
  • Salvador domingo felipe jacinto dali
• Symmetry


  A sense of harmonious and beautiful proportion of balance, invariant in various transformation (reflection, rotation or scaling)
• Two types of symmetry

  • Bilateral symmetry
  • Radial symmetry
• Fractals


  A curve or geometric figure, one of the newest and most exciting branches of mathematics
• Fractals


  • Fractal on leaves
  • Fractal on trees
• Spirals


  A self-similar spiral curve which often appears in nature, described by Rene Descartes and was later investigated by Jacob Bernoulli
• Spirals


  • Spiky shells
  • Spiral worm