Lesson 1

• Mathematics


  The science of numbers and space / The science of measurement, quantity and magnitude
• Mathematics


  • Exact, precise, systematic and a logical subject
• Patterns and numbers in nature repeat again and again
• Patterns are everywhere
• Symmetry


  The math of symmetry can describe what this repetition may look like and as well as why some objects seem more orderly and organized than others
• Symmetry


  Symmetry occurs when there is congruence in dimensions, due proportions and arrangement. It provides a sense of harmony and balance.
• Bilateral or reflection symmetry


  • The simplest kind of symmetry, one of the most common kinds of symmetry that we see in the natural world, an object with this symmetry looks unchanged if a mirror passes through its middle, the objects have a left side and a right side that are mirror images of each other
• Radial symmetry


  • Rotational symmetry around a fixed point known as the center, images with more than one lines of symmetry meeting at a common point exhibits a radial symmetry
• Rosette patterns


  Consist of taking motif or an element and rotating and/or reflecting that element, cyclic if it only admits rotational symmetries, dihedral if it admits both rotational symmetries and bilateral or reflectional symmetries
• Wallpaper pattern


  A pattern with translation symmetry in two directions, essentially an arrangement of friezes stacked upon one another to fill the entire plane, must have at least the basic unit, one copy by translation, and a copy of these two by translation in the second direction, must have at least two rows, each one of at least two units long
• Tessellation or tiling


  A repeating pattern of figures that covers a plane with no gaps or overlaps, just like a wallpaper group in which patterns are created by repeating a shape to fill the plane
• Frieze pattern


  A pattern in which a basic motif repeats itself over and over in one direction
• Fibonacci sequence


  Invented by the Italian Leonardo Pisano Bigollo (1180-1250), also known as Leonardo of Pisa and Fibonacci, Fn := Fn−1 + Fn−2, appears in nature in various places
• Mathematics is everywhere, whether it is on land, sea or air, online or on the front line, mathematics underpins every nook and cranny of modern life
• Roger Bacon (1214-1294): 'Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world'
• Applications of Mathematics in Our World

  • Mathematics helps organize patterns and regularities in the world
  • Mathematics helps predict the behavior of nature and many phenomena
  • Mathematics helps control nature and occurrences in the world for our own good
  • Mathematics has applications in many human endeavors