MAT 152 Mod 2

• PATTERNS in nature are VISIBLE REGULARITIES OF FORM found in the natural world
• Natural Patterns include SYMMETRIES, TREES, SPIRAL, MEANDERS,WAVES,FOAMS,STRIPES and so on...
• (MATH PATTERN IN NATURE)

  ■FRACTAL- Is a DETAILED PATTERN that looks similar at any scale and repeats itself overtime.

  -In nature are SNOWFLAKES, TREES BRANCHING,LIGHTNING and FERNS.

  ■ SPIRAL- Is a CURVED PATTERN

  that focuses on a center of point and a series of circular shapes that revolve around it.

  -In nature are PINE CONES, SOME SHELLS,PINEAPPLES and HURRICANES.

  ■VORONOI- PATTERN PROVIDES CLUES TO NATURE'S TENDENCY to favor efficency

  -The nearest neighbor,shortest path, and tightest fit.

  -In nature are SKIN OF GIRAFFE,CORN ON THE COB,HONEYCOMBS,FOAM BUBBLES and A HEAD OF GARLIC.
• Instead of the word "REPEAT" we use a MATHEMATICAL SYNONYM "ITERATE" and the process is called "ITERATION"
• FIBONACCI SEQUENCE named after the Italian Mathematician LEONARDO FIBONACCI of PISA who in 1202 introduced the sequence.
• Fibonacci Sequence starts with 0 and 1 then every number after that is the sum of the two preceding numbers (0+1=1),(1+1=2),(1+2=3).

  
• A fractal is a SIMPLE pattern repeated over and over.
• What is the rule for this pattern?

  32,36,40,44

  Ans: ADD 4
• What are the three next number in this pattern?

  5,10,15,20,25, _,_,_

  ANS: 30,35,40
• Which pattern follows the rule below?

  Rule: Start with 4 and multiply by 3 each time until there are 4 numbers.

  ANS: 4,12,36,108
• LEONARDO DA PISA- Real name of Fibonacci
• Fibonacci spirals (generated by drawing a quarter-circle in each box, where a larger box lays adjacent to a smaller one, and the lengths of these boxes are Fibonacci numbers) are claimed to appear in the arrangements and patterns of fruits, vegetables, pine cones, seed heads and shells.

  ANS: TRUE
• Fibonacci Pattern

  FORMULA

  xn=xn-1+xn-2

  xn-1 =previous term.

  xn-2 = before that.

  EX: Find the 11th term

  xn=xn-1+xn-2

  x11=x10+x9

  =34+21

  = 55 is the 11th term
• Sequence

  Arithmetic Sequence

  Add and Minus

  
• GEOMETRIC SEQUENCE

  X and ÷

  
• ALGEBRA EQUATION

  
• ans: SIMPLE

  A fractal is a _ pattern repeated over and over.
• SPIRAL a curve starts at a center point and moves away from the center.
• What is a pattern?

  -A group of recurring objects or shapes.