Chapter 1 - MMW

• Mathematics


  • Helps nurture critical thinking, proactiveness, and abstract reasoning
• Mathematics


  The study of the relationships among numbers, quantities and shapes
• Mathematics includes

  • arithmetic
  • trigonometry
  • statistics
  • algebra
  • geometry
  • calculus
• Mathematics provides opportunities to solve both simple and complex problems using a variety of strategies
• Mathematics is a universal way to make sense of the world
• Mathematics helps organize patterns and regularities in the world
• Patterns

  Visible regularities found in the natural world
• Patterns persist in different contexts and can be modeled mathematically
• Natural patterns may consist of

  • spirals
  • symmetries
  • mosaics
  • stripes
  • spots
• Plato, Pythagoras, Empedocles and other Greek Philosophers studied patterns to explain the order in nature which led to the modern understanding of visible patterns
• Joseph Plateau


  Belgian physicist, one of the first people to demonstrate the illusion of a moving image, examined soap films leading him to formulate the concept of minimal space
• Ernst Heinrich Philipp August Haeckel


  Painted hundreds of marine organisms to emphasize their symmetry
• D'Arcy Thompson


  Scottish pioneer who studied growth patterns in both plants and animals, showing that simple equations could explain spiral growth
• Alan Turing


  British mathematician and logician, who predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes
• Aristid Lindenmayer


  Hungarian biologist who showed how mathematics of fractals could create plant growth patterns
• Benoit B. Mandelbrot


  Polish-born, French and American mathematician and polymath, referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry
• W. Gary Smith


  One of North America's leading landscape designers, adopts 8 patterns in his landscape work: scattered, fractured, mosaic, naturalistic drift, serpentine, spiral, radial, and dendritic
• Because of its numerous application, mathemathics became Indespensible
• Without strong math skills, people tend to invest, save, and spend money based on their emotions.
• the essence of mathematics lies in its beauty and its intellectual challenge.
• Shakuntala Devi 


  Without  mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers. 
• Knowledge is power. Information is liberating. Education is the premise of progress, in every society, in every family.
• Leonardo Pisano Bigollo

  Italian mathematician and number theorist; developed Fibonacci Numbers and the Fibonacci Sequence
• Fibonacci 


   Son of Bonacci
• Fibonacci Day


    November 23
• Fibonacci Flowers

  flowers with number of petals that corresponds with the numbers in the Fibonacci sequence
• Fibonacci Sequence


  A number sequence developed by adding two preceding numbers
• The Golden Ratio


  is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.
•  Φ


  The Greek letter “phi “ which is approximately equal to 1.618034
• Golden Spiral


   is a logarithmic spiral whose growth factor is equal to phi
• The mathematics behind symmetry seems to permeate in most of the things around us.
• The mathematics of the pendulum  is quite complicated but harmonic.
• Plane of Mirror

  This regularity in size and distance can be explained mathematically by the law of reflection. 
• free falling object


  is an object that is falling under the sole influence of gravity.
• Newton’s Third Law of Motion


  For every action, there is always an equal opposite reaction
• Language

  • The system of words, signs, and symbols which people use to express ideas, thoughts, and feelings. 
• Natural Language 


  Language that we use everyday to communicate with others (Filipino/English).
• Sentence


   group of words that has complete thought or idea
• Mathemathical Language


  The system used to communicate mathematical ideas
• Mathemathical Nouns

  • Numbers 
  • Measurements
  • Shapes
  • Spaces
  • Functions
  • Patterns 
  • Data 
  • Arrangements