M2

• Fibonacci sequence


  A sequence of numbers where each number is the sum of the two preceding ones, starting with 0 and 1
• Fibonacci sequence


  • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
• Fibonacci sequence


  • Named after Leonardo of Pisa (Fibonacci), who first observed the pattern
  • First two numbers are 1 and 1, each subsequent number is the sum of the previous two
• Fibonacci sequence in nature

  • Seen in sunflower seed heads, sneezewort plants, daisies, cauliflower, pine cones, pineapples
• Golden ratio


  The ratio of two quantities where the ratio of the larger to the smaller is the same as the ratio of their sum to the larger
• Golden ratio


  • Often symbolized by the Greek letter φ
  • Equals (1+√5)/2 ≈ 1.618
• Use of golden ratio

  • Leonardo da Vinci incorporated it in his paintings
• Fibonacci numbers


  Intimately connected to the golden ratio
• Ratios of consecutive Fibonacci numbers converge to the golden ratio
• Mathematics for prediction


  Using mathematical models and patterns to make forecasts and predictions, e.g. weather, astronomy
• Mathematics for control


  Using patterns and mathematical models to understand and control systems, e.g. business analytics, conservation efforts
• It is sometimes said that history repeats itself
• We can use mathematical models using existing data to generate analysis and interpretations, and to make predictions
• Probability


  The chance of an event occurring
• Applications of probability


  • Weather forecasting
  • Predicting meteor showers or eclipses
• In 2017, announcements were made about the Draconid Meteor Shower and "The Great American Eclipse"
• Astronomers were able to tell when these phenomena would occur and where would be the best places to view them
• There seems to be an underlying mathematical structure in the way that natural objects and phenomenon behave
• Mathematics, an invention of the human mind, seems to permeate the natural laws that hold the universe together
• There have been instances when a natural phenomenon has been speculated to exist because mathematics says so but no hard evidence has been found to support its existence
• Such phenomena were proven to exist only when advancements in technology have allowed us to expand our horizons
• In 1916, Albert Einstein hypothesized the existence of gravitational waves based on his theory of general relativity
• About a hundred years later, the Laser Interferometer Gravitational Wave Observatory (LIGO) announced that it found evidence of this phenomenon
• Through the use of mathematics, man is able to exert control over himself and the effects of nature
• The threat of climate change and global warming has been the subject of much debate over the years
• It is believed that unless man changes his behaviour, patterns are said to indicate that sea levels could rise to catastrophic levels as the polar caps melt due to the increase in global temperatures
• To ensure that greenhouse gas concentrations in the atmosphere are kept that would not interfere with the climate system, the United Nations Framework Convention on Climate Change (UNFCCC) was signed in 1992 and has 197 parties as of December 2015
• Albert Einstein: 'How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of reality?'
• Mathematics serves as the foundation for logical thinking and reasoning
• Mathematics equips individuals with critical thinking skills, enabling them to approach problems systematically and make sound judgments based on evidence and analysis
• 10 Reasons why Math is Important to Life

  • Learning math is good for your brain
  • Math helps you tell time
  • Math helps you with your finances
  • Math makes you a better cook (baker)
  • Math helps us have better problem-solving skills
  • Math is used in practically every career in some way
  • Math is all around us and helps us understand the world better
  • Math can make you more popular
  • Math can help you shop a good sale
  • Math is the universal language
• Math is not only important for success in life, it is all around us
• The laws of mathematics are evident throughout the world, including in nature
• The problem-solving skills obtained from completing math homework can help us tackle problems in other areas of life
• Can you see anything special about these ratios?
• Robert Langdon


  The hero of Dan Brown's best-selling novel The Da Vinci Code
• Langdon's specialty is religious symbology
• Langdon figured out the message

  The words are anagrams for "Leonardo da Vinci" and "the Mona Lisa"
• The numbers are the first eight members of the Fibonacci sequence, written in a jumbled order
• Fibonacci sequence


  One of the most famous mathematical sequences