Gec 4

• Johannes kepler


  -a German astronomer, discovered "the six- cornered snowflake"

  -he believed that snowflakes are formed when small identical units bind together like atoms.
• Fractals 


  -extremely irregular curves or shapes.
• Symmetry 


  -harmonious and beautiful proportion of balance.
• Bilateral symmetry


  -formed when organism is divided into two and the left side.
• Radial or Rotational symmetry


  -a type of symmetry around a fixed point.
• Spiral


  -plane curve that winds around a central point.
• Stripes 


  -line or long narrow section.
• Cracks


  -lineare openings that form in materials to relieve stress.
• Tesselations 


  -repeating tiles all over a flat surface.
• Bubble 


  -a tiny, round ball of air and gas inside a liquid.
• Foam


  -a mass of bubbles
• Waves


  -are disturbance that carry energy as they move.
• Ripples 


  -are created when waves in water or wind pass over sand.
• Dunes


  -are formed when wind blows over large bodies of sand.
• Fibonacci sequence 


  -adding up the two numbers before it.

  -discovered by Leonardo Bigollo or Fibonacci which translated "Filius Bonacci" meaning "Son of Bonaccio". In his book "Liber Abaci".
• Mathematics 


  -involves the study and  arithmetic operations.

  -defined as the set of problem- solving tools, a process, a study of patterns and an art.
• Mathematics 


  -is an science that involves logical reasoning, drawing conclusions from assumed premises and strategic reasoning based on accepted rules, laws and possibilities.
• Forensic science


  -crime investigation and evidence examination
• Forensic science 


  -in this field, mathematics, specially the differential and integral calculus is applied to clarify the blurred image to clear image.
• Medicine 


  -in this field, much of a function of a protein is determined by its shaped and how the pieces move. Many drugs are designed to change the shape or motions of a protein by modelling using geometry and related areas.
• Fluid dynamics 


  -describes the flow of fluids- liguid and gases
• Fluid dynamics 


  -In this field, engineers use numeral analysis in phenomena involving heat, electricity, and magnetism, relatistic mechanics, quantum mechanics, and other theoretical constructs.
• Information technology


  -in this field, modern computers are invented through the help of mathematics. An important area of applications of mathematics.
• Cryptography 


  -hiding or coding information
• Cryptography 


  -It is combination of both mathematics and computer science and is affliated closely with information theory, computer security and engineering. It is used i aplication pesent i technologically advanced societies; examples include the security of ATM cards, computer passwords and electronic commerce.
• Archeology 


  -In this field, they uses a variety of mathematical and statistical techniques to present the data from archeological surveys an try to find patterns to shed light on past human behavior and in carbon dating artifacts.
• Social science 


  -economics, sociology, psychology, linguistic, etc.
• Social science 


  -in this field, calculus, probability, game theory, and network theory were used in economics, sociology psychology, and linguistic.
• Political science 


  -in this area, political analyst study past electron results to see changes in voting patterns and the influence of various factors on  voting behavior, on switching of votes among political parties and mathematical models for conflict resolution using game theory and statistics.
• Music and arts


  -Here, the rhythm that we find in all music notes is the result of innumerable permutations and combinations. Music theorists understand musical structure and communicate news ways of hearing music by applying set theory, abstract algebra, and number theory.
• Set theory


  -it is the branch of mathematics that studies sets or the mathematical science of infinite.
• George Cantor


  -a mathematician in the 19th century, that introduced the set theory.
• Set


  -it is a collection of well defined distinct objects.
• Element 


  -the object that make up set
• Roster method 


  -or Tabulation Method

  -tge elements of a set are listed and seoarated by commas and enclosed in braces. Example M={1,2,3,4,5,6,7}.
• Rule method 


  -or Set- Builder Notation

  -it indicates a set by enclosing in braces a descriptive phrase, and agreeing that object, and only those, which have described properly are the elements of the set. Example N={x/x is an even numbers less than 10}.
• Finite


  -possibility of writing down a complete list of all elements of the set.
• Infinite


  -impossibility of writing down all elements of the set.
• Unit set 


  -a set with only one element
• Empty set


  -The unique set with no elements and is denoted.