Pattern in Nature.ppt

PATTERNS IN NATURE MATHMW 1 AUGUST Let’s target: 1. identify patterns in nature and regularities in the world, 2. expound on the nature of mathematics, what is it, how it is expressed, represented, and used. 3. describe how to create the Fibonacci sequence, 4. identify instance...

PATTERNS IN NATURE MATHMW 1 AUGUST Let’s target: 1. identify patterns in nature and regularities in the world, 2. expound on the nature of mathematics, what is it, how it is expressed, represented, and used. 3. describe how to create the Fibonacci sequence, 4. identify instances where the Fibonacci sequence and its derivatives, the Golden Mean, Golden Ratio, the Golden Spiral, and the Golden Rectangle, are manifested; and, 5. explain and appreciate the importance and presence of the patterns and regularities and the Fibonacci sequence. Arrange the letters to form the words relative to patterns in CARFSLAT FRACTALS It is a detailed pattern that looks similar at any scale and repeats itself over time. It gets more complex as it is observed at larger scales. Examples: snowflakes, trees branching, lightning, ferns FRACTALS INOROVO VORONOI Itprovides clues to nature’s tendency to favor efficiency: the nearest neighbor, shortest path, and tightest fit. Examples: skin of a giraffe, corn on the cob, honeycombs, foam bubbles, the cells in a leaf VORONOI It provides clues to nature’s tendency to favor efficiency: the nearest neighbor, shortest path, and tightest fit. Examples: skin of a giraffe, corn on the cob, honeycombs, foam bubbles, the cells in a leaf RAPILSS SPIRALS Itis a curved pattern that focuses on a center point and a series of circular shapes that revolve around it. Examples: pine cones, pineapples, hurricanes SPIRALS Itis a curved pattern that focuses on a center point and a series of circular shapes that revolve around it. Examples: pine cones, pineapples, hurricanes LLSSTEEATIO N TESSELLATIO N It is a design or pattern in which a shape is used repeatedly to cover a plane with no gaps, overlaps, or empty spaces. KINDS OF TESSELLATION 1. Regular 2. Semi-regular 3. Irregular IRREGULAR TESSELLATION TRYMMESY SYMMETRY Symmetry is when different sides of something are alike. This produces mirror images with only two sides, like the two sides of our bodies; they may be symmetrical on several sides, like the inside of an apple sliced in half; or they might be symmetrical on all sides, like the different faces of a cube. FORSNARTTION MA TRANSFORMAT ION A transformation changes a figure into another figure. The new figure formed by a transformation is called the image. In some transformations, the figure retains its size and only its position is changed. Kinds of Transformation 1. Reflection 2. Rotation 3. Translation 4. Dilation What is the Golden Rule? SYMMETRY Symmetry is when different sides of something are alike. This produces mirror images with only two sides, like the two sides of our bodies; they may be symmetrical on several sides, like the inside of an apple sliced in half; or they might be symmetrical on all sides, like the different faces of a cube.