This course deals with the nature of mathematics, appreciation of its practical, and aesthetic dimensions, and application of mathematical tools in daily life

Mathematics in the modern world

1. MATHEMATICS IN THE MODERN WORLD

2. What is mathematics? Formal system of thought for recognizing, classifying, and exploiting patterns The origins of counting Geometric patterns Wave patterns in water and on land Patterns of movement Fractals

3. Where is mathematics? We see hints or clues of it … In nature In our daily routine In our world In people and communities In events

4. What is mathematics for? To help us unravel the puzzles of nature, a useful way to think about nature Organize patterns and regularities as well as irregularities To be able to predict To help us control weather, epidemics Provides tools for calculations Provides new questions to think about

5. What is mathematics about? Numbers, symbols, notations Operations, equations, and functions Processes and “thingification” of processes (that are abstractions, e.g., 3) Proof – a story rather than a sequence of statements

6. How is mathematics done? With curiosity With a penchant for seeking patterns and generalities With a desire to know the truth With trial and error Without fear of facing more questions and problems to solve With tenacity (willingness to keep working)

7. Who uses mathematics? Mathematicians: pure and applied Scientists: natural and social Practically everyone But different people use different math at different times, for different purposes, using different tools with different attitudes

8. Why is mathematics important to know? It puts order in disorder It helps us become better persons It helps the world a better place to live in

9. Most talented mathematician of the middle ages Born: 1170, Pisa, Italy Died: 1250, Pisa, Italy Name: Leonardo Bonacci Also known as . . . Leonardo of Pisa Leonardo Pisano Bigollo Leonardo Fibonacci Popularly known as FIBONACCI

10. If two new rabbits are put in a pen, How many r abbits will b e in the pen after one year? In 1202, Fibonacci wrote a very famous book “ Liber abaci” to describe mathematics he learned.

11. Assume that rabbits... ... always produce one male and one female offspring . ... can reproduce once every month. ... can reproduce when they are one month old. ... never die! “If 2 new born rabbits are put in a pen, how many rabbits will be in the pen after one year?” Your Task: Work with your seatmate and create an illustration (tree diagram, table, flowchart, etc) on how the rabbit population expanded over a year.

12. http://britton.disted.camosun.bc.ca/fibslide/fib00.jpg

13. White Calla Lily: http://britton.disted.camosun.bc.ca/fibslide/fib01.jpg

14. Euphorbia: http://britton.disted.camosun.bc.ca/fibslide/fib02.jpg

15. Trillium: http://britton.disted.camosun.bc.ca/fibslide/fib03.jpg

16. Columbine: http://britton.disted.camosun.bc.ca/fibslide/fib04.jpg

17. Bloodroot: http://britton.disted.camosun.bc.ca/fibslide/fib05.jpg

18. Black-eyed susan : http://britton.disted.camosun.bc.ca/fibslide/fib06.jpg

19. Shasta Daisy with 21 petals: http://britton.disted.camosun.bc.ca/fibslide/fib07.jpg

20. Field daisies with 34 petals: http://britton.disted.camosun.bc.ca/fibslide/fib08.jpg

21. The Fibonacci sequence in plants Count the number of branches per generation.

22. The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . How many rabbits are there on the 13 th month? 14 th month? Can you state the rule on how to get a term of the sequence?

23. The Fibonacci SURPRISE! 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . What can you say about every third term ? What can you say about every fourth term ? What can you say about every fifth term ?

24. MORE SURPRISES! 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . Try adding together any three consecutive Fibonacci numbers. What do you notice? Can you explain it? Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two. What do you notice? Can you explain it? Discover any surprise of your own.

25. Fruits A banana has 3 sections An apple has 5 sections Fabulous Fibonacci: http://fabulousfibonacci.blogspot.com/

26. Pineapple Fabulous Fibonacci: http://fabulousfibonacci.blogspot.com/

27. Cauliflower Fabulous Fibonacci: http://fabulousfibonacci.blogspot.com/

28. http://www.gettyimages.com/detail/photo/cone-of-pine-royalty-free-image/108820976

29. http://www.gettyimages.com/detail/photo/top-view-of-a-brown-pine-cone-on-a-white-background-royalty-free-image/172978445

30. http://www.gettyimages.com/detail/photo/hawaii-oahu-diamond-head-sunflower-close-up-high-res-stock-photography/601204276

31. https://www.123rf.com/photo_7987120_sunflower-seedheaad-pattern-fibonacci.html

32. https://www.shutterstock.com/image-photo/lily-flowers-on-white-background-252724396?irgwc=1&utm_medium=Affiliate&utm_campaign=Nguyen%20Duy%20Phi&utm_source=38874

33. http://www.gettyimages.com/detail/photo/buttercups-summer-sun-royalty-free-image/172368337

34. http://www.gettyimages.com/detail/photo/close-up-of-yellow-back-eyed-susan-flower-royalty-free-image/562845269

35. http://www.gettyimages.com/detail/photo/close-up-of-beautiful-dutch-iris-royalty-free-image/159594206

36. http://www.gettyimages.com/detail/photo/aster-royalty-free-image/185089362

37. http://www.gettyimages.com/detail/photo/yellow-cauliflower-royalty-free-image/186828825

38. http://www.gettyimages.com/detail/photo/yellow-cauliflower-royalty-free-image/186828825

39. https://www.noupe.com/inspiration/photography/nature-s-pattern-photography-35-outstanding-photos.html

40. https://www.noupe.com/inspiration/photography/nature-s-pattern-photography-35-outstanding-photos.html

41. https://www.noupe.com/inspiration/photography/nature-s-pattern-photography-35-outstanding-photos.html

42. https://www.noupe.com/inspiration/photography/nature-s-pattern-photography-35-outstanding-photos.html

43. http://www.gettyimages.com/detail/photo/bees-royalty-free-image/157643400 https://www.extremetech.com/extreme/172357-the-most-beautiful-snowflake-photos-youll-ever-see-captured-with-a-cheap-diy-camera