GEOMETRY IN OUR LIVES � Part I

GEOMETRY IN OUR LIVES – Part I Our daily lives are crammed full of objects we use constantly, designed with precise geometric shapes. The Clothoid. The Cycloid. The Catenary. The Helix. - The discovery and origin of Geometry - Some of the practical use of Mathematics - Mathematics an important tool for many other Scienes (Physics, Medicine, Chemistry, Civil Engineering, Architecture, Computer Science, etc.) Common Geometric Forms – Man’s creativity and Geometry - The innumerable shapes - The Circumference – the circle - Isoperimetricty - The sphere – why are many water and fuel tanks spherical? - Why are many astronomical bodies with high masses spherical? Cones and other curves - How is a conical curve obtained. - Circumference - Ellipse - Parabola - The orbits of planets are elliptical - Hyperbolas - The Square of Saint Peter at the Vatican - San Francisco’s Golden Gate Bridge : its impressive parabolas - Applications of the conical section - The acoustic property of ellipses and parabolas. The Room of Secrets in the Alhambra, Granada, Spain and St. Paul’s Cathedral, London, UK - Three dimensions parabolas - The shape of motorways and high speed train tracks - Clothoid or Cornu’s Spiral often used in civil engineering - What is a cycloid - What is a catenary . The Saint Louis Gateway Arch in Missouri, USA - Gaudí and the catenary. Casa Milá in Barcelona, Spain - The Helix Geometry in Art - The use of geometric figures in art particularly in Islamic art - Some examples of geometric art - The Islamic mosaics : transformation and rotation of polygons - Fedorov Arab Mathematician and his theory of “flat christallorgraphic groups” - The Alhambra decorated with the 17 basic flat geometric decorative patterns More practical applications of Geometry - Topography - Civil engineering and architecture - The Global Positioning System (GPS). - Television, communications networks, agriculture, petrol and gas prospecting - Land, sea and air transport - The GPS : how does it work