MODULE 1 SYMMETRIES

• The mathematics in our world is rooted in patterns
• Patterns are all around

  us
• A pattern is a structure, form, or design that is regular, consistent, or recurring. It can be found in nature, in human-made designs, or in abstract ideas. They occur in different contexts and various forms.
• Kinds of Pattern, Visual, Flow, Movement, Rhythm, texture, geometric patterns
• Patterns of Visuals. are often unpredictable, never

  quite repeatable, and often contain fractals.
• Patterns of Flow. The flow of liquids provides an inexhaustible supply of nature’s patterns.
• Patterns of Movement. In the human walk, the feet strike the ground in a

  regular rhythm: the left-right-left-right-left rhythm
• Patterns of Rhythm. is conceivably the most basic pattern in nature.
• Patterns of Texture. is a quality of a certain object that we sense

  through touch. It exists as a literal surface that we can feel, see, and imagine.
• Geometric Patterns. A is a kind of pattern which consists of

  a series of shapes that are typically repeated.
• Kind of Symmetries, Reflection Symmetry, Rotations, Translations
• Reflection symmetry, sometimes called line symmetry or mirror

  symmetry, captures symmetries when the left half of a pattern is the same

  as the right half.
• Rotations, also known as rotational symmetry, captures symmetries when it still looks the same after some rotation (of less than one full turn). The degree of an object is recognized by the number of distinct orientations in which it looks the same for each rotation.
• Translations. This is another type of symmetry. It exists in patterns that we see in nature and in man-made objects. it acquire symmetries when units are repeated and turn out having identical figures.
• In describing the amazing variety of phenomena in nature we stumble to discover the existence of Fibonacci numbers
• It turns out that the Fibonacci numbers

  appear from the smallest up to the biggest objects in the natural world.