MIDTERM (MATHEMATICS IN MODERN WORLD)

• IVG


  What completes the following pattern? CSD, ETF, GUH,_______, KWL
• Set


  A well defined collection of objects or elements.
• Disjoint Set


  Two sets that do not share any common element.
• Unit

  A set with only one element.
• Equivalent


  Two sets that contain the same number of elements.
• Finite


  A set that contains a countable number of elements.
• Golden Rectangle


  A rectangle where the ratio of the longer side to the shorter side is equal to the golden ratio.
• 1.6180


  The approximate value of the golden ratio, represented by the Greek letter (phi)
• Fibonacci Sequence


  A sequence of numbers where each term is the sum of two preceding one, and its ratio of consecutive terms approaches the golden ratio as the sequence progresses.
• Parthenon


  A famous structure in Greece, often cited as an example of the golden ratio applied in achitecture.
• Rhythm


  It said to be the most basic pattern in nature.
• Geometric


  What kind of pattern is a series of shapes that are repeating?
• Leonardo Da Vinci


  The famous Renaissance artist and polymath who used the golden ratio in his works and studies of human proportions.
• Deductive Reasoning


  The type of reasoning used when solving puzzle or mystery by plecing together clues to form a logical conclusion.
• Inductive


  A form reasoning where conclusions are considered probable, but not guaranteed, even if the premises are true.
• Pattern of Visuals


  Are often predictable never quite repeatable, and often contain fractals.

  • Examples in seeds and pinecones to the branches and leaves.
• Patterns of Flow


  The flow of liquids provides an inexhaustible supply of nature’s patterns. Patterns of flow are usually found in the water, stone, and

  even in the growth of trees.
• Patterns of Movement. In the human walk, the feet strike the ground in a

  regular rhythm: the left-right-left-right-left rhythm. When a horse, a four-

  legged creature walks, there is more of a complex but equally rhythmic pattern.
• Patterns of Rhythm. Rhythm is conceivably the most basic pattern in nature.

  Our hearts and lungs follow a regular repeated pattern of sounds or

  movement whose timing is adapted to our body’s needs.
• Patterns of Texture. A 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 geometric pattern is a kind of pattern which consists of

  a series of shapes that are typically repeated.
• Patterns found in Nature

  -Spots and Stripes

  -Spirals
• Symmetry - indicates that you can draw an imaginary line across an object

  and the resulting parts are mirror images of each other.
• sometimes called line symmetry or mirror symmetry, captures symmetries when the left half of a pattern is the same as the right half.
• Rotational Symmetry

  Spiderwort with three-fold symmetry

  Starfish five-fold symmetry
• Order of Rotation (Formula)

  
• Translations - It exists in patterns that we see in nature and man-made objects. Translations acquire symmetries when units are repeated and turn out having identical figures.
• Symmetries in Nature

  Leonardo da Vinci’s Vitruvian Man showing the proportions and symmetry of the human body
• Symmetries in Nature
• Snowflake six-fold symmetry
• A sequence is an ordered list of numbers, called terms, that

  may have repeated values. The arrangement of these terms is

  set by a definite rule.
• Types of Sequence

  1. Arithmetic Sequence
  2. Geometric Sequence
  3. Harmonic Sequence
  4. Fibonacci Sequence
• The Fibonacci numbers or sequence are the numbers in the following integer sequence:

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

  And on this sequence we could see that there would be what we called the Golden Ratio.
• FORMULA FOR FIBONACCI SEQUENCE

  
• Golden Ratio and Golder Rectangle with Spiral

  
• According to Ivanka Stipancic-Klaic and Josipa Matotek of the University of Osijek, Croatia, the Golden ratio fascinates and intrigues not only

  mathematicians, but also artists, architects, biologists, philosophers and

  musicians. This golden ratio was first studied by the ancient Greek because of its frequent appearance in geometry.
• The development of the idea of the golden ratio is usually attributed to

  Pythagoras (580-497 BC) and his students. It is often represented by the

  Greek letter τ (tau) which means “the cut” or “the section” in Greek. But,

  Mark Barr (early 18th century) represented the golden ratio as φ (phi)

  because it is the first letter in the name of Greek architect and sculptor Phidias who’s work often symbolized the golden ratio.
• The ratio is came from to a line segment divided according to the golden

  ratio where the larger part is to the smaller part as the whole part is to the larger part, thus;

  
• Approximate vale of phi

  
• Golden Ratio can be seen also in the Fibonacci number.