Patterns and Numbers in nature and the World.pptx

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1. Patterns and Numbers in nature

2. WHAT DOES MATHEMATICS HAVE TO DO WITH NATURE? The natural world is full of beauty and amazing shapes and patterns. In his book, Nature by Numbers, Ian Stewart mentioned that we live in a universe of patterns. If you observe our nature diligently, you can prove that our nature bounds in mystical colors and intricate shapes and patterns that can be described mathematically.

3. WHAT MATHEMATICS IS ABOUT AND WHAT IT IS FOR? - Numbers are the heart of mathematics; - Mathematics makes our life orderly and systematic, and it prevents chaos; -It can be used to express, solve, and interpret the puzzles observed in nature; - It helps us to see patterns needed to generalize a broader solution to a problem.

4. WHAT MATHEMATICS IS ABOUT AND WHAT IT IS FOR? - It expounds the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem solving ability, and even effective communication skills.

5. Patterns Patterns are repetitive, which can be found in nature as color, shape, action, or some other sequences that are almost everywhere. Mathematics expresses patterns. These sequences that repeat, follows a rule or rules. A rule is a way to calculate or solve a problem.

6. Patterns - Natural patterns include symmetries, fractals, spirals, meanders, waves, foams, tessellations, cracks, and stripes. Studying patterns allows one to watch, guess, create, and discover.

7. 1. Symmetry is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

8. a. Reflection or Bilateral - It is also called mirror symmetry or line symmetry. It is made with a line going through an object which divides it into two pieces which are mirror images of each other.

9. b. Radial Symmetry - Radial symmetry is rotational symmetry around a fixed point known as the center.

10. Radial Symmetry

11. c. Translational Symmetry - This kind of symmetry is exhibited by objects which do not change its size and shape even if it moved to another location. Note that the movement does not involve with reflection or rotation.

12. 2. Fractals These are never-ending patterns that are self-similar across different scales. The image just reappears repeatedly no matter how many times the object is magnified.

13. 3.Spirals These are curved patterns made by series of circular shapes revolving around a central point.

14. 4. Spots and stripes Patterns are also exhibited in the external appearances of animals.

15. 5. Flower Petals Flowers are easily considered as things of beauty. Their vibrant colors and fragrant odors make them very appealing as gifts or decorations.

16. 6. Number Patterns and Sequences Consider the pattern below.

17. Leonardo Pisano Bigollo Fibonacci (1170~1240) FIBONACCI SEQUENCE

18. Fibonacci Sequence The Fibonacci numbers are a series of number that often occur in nature. To formally, define the Fibonacci sequence, we start by defining F1 = 1 and F2 = 1 . For n > 2 , we define,  

19. Example If we take the ratio of Fn to Fn−1 for n ≥ 1, n n 1 1 8 21 2 1 9 34 3 2 10 55 4 3 11 89 5 5 12 144 6 8 13 233 7 13 14 377 n n 1 1 8 21 2 1 9 34 3 2 10 55 4 3 11 89 5 5 12 144 6 8 13 233 7 13 14 377

20. Example If we take the ratio of Fn to Fn−1 for n ≥ 1 , n n 1 1 - 8 21 1.61538… 2 1 1 9 34 1.61904… 3 2 2 10 55 1.61764… 4 3 1.5 11 89 1.61818… 5 5 1.666… 12 144 1.61797… 6 8 1.6 13 233 1.61805… 7 13 1.625 14 377 1.618025… n n 1 1 - 8 21 1.61538… 2 1 1 9 34 1.61904… 3 2 2 10 55 1.61764… 4 3 1.5 11 89 1.61818… 5 5 1.666… 12 144 1.61797… 6 8 1.6 13 233 1.61805… 7 13 1.625 14 377 1.618025…

21. Example we see that as n gets larger and larger, the ratio gets closer and closer to a value denoted by . The number is called as the golden ratio and can be formally defined as  

22. Mathematics for our world

23. Mathematics is everywhere; whether it is on land, sea or air, online or on the front line, mathematics underpins every nook and cranny of modern life. Far from a quaint subject to be forgotten upon leaving school, it is the glue that holds our world.

24. Roger Bacon (1214-1294), an English Franciscan friar, philosopher, scientist and scholar of the 13th century, once stated: “Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.”

25. Application of Mathematics in our World

26. Mathematics helps organize patterns and regularities in the world; According to Ian Stewart (1995), we live in a universe of patterns. Human mind and culture have developed a formal system of thought for recognizing, classifying and understanding patterns.

27. Mathematics helps predict the behavior of nature and many phenomena Mathematics is used to explain why the Sun set, where it went and why it returned because it was easier to count these events in numbers than to put them into words. Based on historical patterns, we can make forecasts or predictions to help us prepare for our daily activities.

28. Mathematics helps control nature and occurrences in the world for our own good. Mathematical modelling and control theory can be used. By mathematical modeling we see the inputs to events and their most likely outcomes.

29. Mathematics has applications in many human endeavors making it indispensable Mathematics existed since the beginning of time, written or unwritten. Its unwritten history is carved in all things found in cosmos , found in the patterns created in nature, appreciated in the juxtaposition of the heavens and the earth, contrast between darkness and light , made sense in the harmony created not just by a well-known orchestra but even by the rain drops falling on offshore wind-turbines.

30. WHAT IS IT? PERIMETER The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

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