MATHEMATICS IN THE MODERN WORLD Module 2.pptx

RECOGNIZING PATTERNS IN NATURE AND CONFIGURATIONS IN THE WORLD

1. MATHEMATICS IN THE MODERN WORLD MODULE #2 RECOGNIZING PATTERNS IN NATURE AND CONFIGURATIONS IN THE WORLD

2. MATH PATTERNS IN NATURE *FRACTAL *SPIRAL *VORONOI

3. FRACTAL A fractal is a detailed pattern that looks similar at any scale and repeats itself over time. A fractal's pattern gets more complex as you observe it at larger scales. This example of a fractal shows simple shapes multiplying over time, yet maintaining the same pattern. Examples of fractals in nature : snowflakes, trees branching, lightning, and ferns.

4. SPIRAL A spiral is a curved pattern that focuses on a center point and a series of circular shapes that revolve around it. Examples of spirals are pine cones, pineapples, hurricanes.

5. VORONOI A Voronoi pattern provides clues to nature’s tendency to favor efficiency: the nearest neighbor, shortest path, and tightest fit. Each cell in a Voronoi pattern has a seed point. E xamples of Voronoi patterns are the skin of a giraffe, corn on the cob, honeycombs, foam bubbles, the cells in a leaf, and a head of garlic.

6. PATTERNS: Watch: https://vimeo.com/9953368

7. FIBONACCI SEQUENCE

8. FIBONACCI SEQUENCE The Fibonacci sequence named after the Italian mathematician Leonardo Fibonacci of PIsa . His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy. "Fibonacci" was his nickname, which roughly means "Son of Bonacci" , who in 1202 introduced the sequence. It turns out that simple equations involving the Fibonacci numbers can describe most of the complex spiral growth patterns found in nature.

9. RULE OF FIBONACCI SEQUENCE The Fibonacci Sequence can be written as a "Rule" . First, the terms are numbered from 0 onwards like this: So term number 6 is called x 6 (which equals 8).

10. RULE OF FIBONACCI SEQUENCE So we can write the rule: The Rule is x n = x n −1 + x n −2 where: x n is term number "n" x n −1 is the previous term (n−1) x n −2 is the term before that (n−2)

11. MAKE A SPIRAL When we make squares with those widths, we get a nice spiral: Do you see how the squares fit neatly together? For example 5 and 8 make 13, 8 and 13 make 21, and so on.

12. REFERENCES: https://www.fi.edu/math-patterns-nature https://www.mathsisfun.com/numbers/fibonacci-sequence.html