The Nature of Mathematics

Mathematics is a useful way to think about nature and our world.

1. The Nature of Mathematics By Prof. Liwayway Memije -Cruz

2. What is mathematics? Where is mathematics? What role does mathematics play in your world?

3. Mathematics is the study of pattern and structure.

4. Many patterns and occurrences exist in nature, in our world, in our life. Mathematics helps makes sense of these patterns and occurrences. Mathematics is a tool to quantify, organice and control our world, predict phenomena and make life easier for us.

5. Mathematics is fundamental to the physical and biological sciences, engineering and information technology, to economics and increasingly to the social sciences.

6. Mathematics is a useful way to think about nature and our world.

7. Nature

8. Snowflakes

9. Honeycomb

10. Tiger’s stripes

11. Hyena’s spots

12. Sunflower

13. Snail’s shell

14. Flower petals

15. World population

16. Weather

17. Topics: Mathematics in our World Fibonacci Numbers Golden Ratio

18. Fibonacci: Leonardo Pisano An Italian mathematician from the Republic of Pisa, who is considered to be "the most talented Western mathematician of the Middle Ages".

19. Looking at simple things deeply, finding a pattern, and using the pattern to gain new insights provides great value.

20. Sequences of Numbers The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it. The 2 is found by adding the two numbers before it (1+1) The 3 is found by adding the two numbers before it (1+2), And the 5 is (2+3), and so on!

21. The Fibonacci Sequence 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610; 987; 1597; 2584; 4181; 6765; 10946; 17711; 28657; 46368; 75025; 121393; 196418; 317811; 514229; 832040; 1346269; 2178309; 3524578; 5702887; 9227465; 14930352; … The first 2 numbers are 1 and subsequent numbers are obtained by adding the previous two numbers.

22. The Rule x n = x n-1 + x n-2 Where: Xn is term number "n" Xn-1 is the previous term (n-1) Xn-2 is the term before that (n-2)

23. Makes 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.

24. Honeycomb: a mass of hexagonal wax cells built by honeybees

25. The Golden Rule

26. Golden Ratio a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form, it looks like this: a/b = ( a+b )/a = 1.6180339887498948420 …

27. phi the ratio of the circumference of a circle to its diameter. usually rounded off to 1.618. Golden mean, the Golden section, divine proportion, can be seen in the architecture of many ancient creations, like the Great Pyramids and the Parthenon

28. The Golden ratio also appears in all forms of nature and science. Some unexpected places include:

29. Flower petals: The number of petals on some flowers follows the Fibonacci sequence. It is believed that in the Darwinian processes, each petal is placed to allow for the best possible exposure to sunlight and other factors .

30. Seed heads The seeds of a flower are often produced at the center and migrate outward to fill the space. For example, sunflowers follow this pattern.

31. Pinecones The spiral pattern of the seed pods spiral upward in opposite directions. The number of steps the spirals take tend to match Fibonacci numbers.

32. Tree branches The way tree branches form or split is an example of the Fibonacci sequence. Root systems and algae exhibit this formation pattern.

33. Shells Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral .

34. Spiral galaxies The Milky Way has a number of spiral arms, each of which has a logarithmic spiral of roughly 12 degrees. The shape of the spiral is identical to the Golden spiral, and the Golden rectangle can be drawn over any spiral galaxy.

35. Hurricanes Much like shells, hurricanes often display the Golden spiral.

36. DNA molecules A DNA molecule measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral. In the Fibonacci series, 34 and 21 are successive numbers.

37. Animal bodies The measurement of the human navel to the floor and the top of the head to the navel is the Golden ratio. But we are not the only examples of the Golden ratio in the animal kingdom; dolphins, starfish, sand dollars, sea urchins, ants and honeybees also exhibit the proportion.

38. Fingers The length of our fingers, each section from the tip of the base to the wrist is larger than the preceding one by roughly the ratio of phi.

39. References: https://www.mathsisfun.com/numbers/fibonacci-sequence.html https://www.livescience.com/37704-phi-golden-ratio.html https://www.mathsisfun.com/numbers/golden-ratio.html https://math.temple.edu/~reich/Fib/fibo.html