GEOMETRY IN OUR LIVES � Part II

GEOMETRY IN OUR LIVES – Part II The number PHI Φ.The Fibonacci Series. The Egyptians and the Greeks. Fractals. Topology. - A mysterious number…the “golden section, ratio or mean” is everywhere - The golden number: PHI Φ . The most remarkable properties. The Golden number in art and design - The pyramid of Kheops - The Greeks knew the golden number and used it profusely in temples and sculptures - Phidias the famous Greek sculptor - Use of the number Phi Φ by artists, painters, architects and sculptors (Leonardo da Vinci, Michael Angelo, etc. ) - Le Corbusier and the golden number - The golden number and other artistic expressions such as poetry and music. - The musical notes of the Sol-Fa musical scale and the golden number - The mythical Stradivarius violins and the golden number - The Pentagon and the Phi Φ - Today’s logos design and the golden number - The golden number and the Fibonacci Series The Golden Number in nature - Nature: the Kingdom of Phi Φ - The Sunflowers - The spikes of common pineapples - The number of petals in many flowers - The branches and leaves of plants - Influence of the golden number in the growth of shellfish - Growth of the horns of some ruminants - The shape of tropical cyclones and spiral galaxies - The human body Fractals - Traditional forms of Euclidean geometry (rectangles, circumferences, polygons, etc.) - What are fractals? Applications of fractals - How to obtain a fractal - The Mandelbrot Set - Fractal: the geometry of nature - Fractal structures - The use of fractal geometry - Applications of fractals in medicine “Rubber Sheet” Geometry - What is Topology? - Circumference and a lemniscate The Graph Theory - Leonhard Euler and the origins of topology - Applications of the theory of Graph: telecommunications networks: fixed phones and cell pones, Internet, digital TV, etc. - Applications of the theory of Graph in the study of the urban and interurban transport networks, bus and metro networks - Electrical circuits - Changing our perspective slightly to discover that numbers and geometric shapes are more intimately linked to us than we’d ever imagined