Module 1: The Nature of Mathematics

• " The world we cannot move even an inch without mathematics"

  Ian Stewart
• Types of Patterns

  1. Symmetry
  2. Fractals
  3. Spirals
  4. Spot and Stripes
  5. Flower Petals
  6. Number Patterns and Sequences
• Kinds of Symmetry

  1. Reflection Symmetry
  2. Rotational Symmetry
  3. Translational Symmetry
• Symmetry


  Is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.
• Reflection symmetry

  Also called Mirror Symmetry or a Line Symmetry. often termed as Bilateral Symmetry as it divides the object into 2 (bi) mirror images.
• Rotational Symmetry

  A radial symmetry. in biology, this kind of symmetry is exhibited by objects when their similar parts are regularly arranged around a central axis.
• Translational Symmetry


  Exhibited by objects which do not change its size and shape even if it moved to another location.
• Fractals


  are never ending patterns that are self-similar accross different scales. The image just reappears over and over again no matter how many times the object is magnified.
• Spirals


  These are curved patterns made by series of circular shapes revolving around a central point.
• Spot and Stripes


  exhibited in the external appearances of animals.
• FLOWER PETALS


  are easily considered as things of BEAUTY.

  Their vibrant colors and fragrant odors make them very appealing as gifts or decorations.

  The common number of petals is 5.
• Patterns


  are regular, repeated, or recurring forms or designs.
• Word Patterns


  focused on the morphological rules in pluralizing nouns, conjugating verbs for tense, and metrical rules of poetry.
• Geometric Patterns


  are designs that depict geometric shapes like lines, circles, and polygons. Geometric patterns are observed in nature. These patterns are also associated with the identification of a particular country and culture.
• Observe that if we rotate the flower and the starfish by several degrees, we can still have same appearance as the original position. This is called

  Rotational symmetry
• The smallest angle an object can be rotated while it is preserving its original formation is called the

  Angle of Rotation
• To compute the angle of rotation, we use

  $angle of rotation=$$360*$$/n$
• Fibonacci Sequence


  is a short term sequence for the latin "filius Bonacci", which means "son of bonacci".
• A sequence of numbers in which each number is increased by the same amount.

  Arithmetic
• Each number is the sum of the 2 numbers before it.

  Fibonacci
• A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

  Geometric
• add the same amount each time

  Arithmetic
• Multiplying by the same number each time.

  Geometric