Mathematics in Nature
Published on Nov 18, 2015
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Math
In Nature
Fibonacci
Sequence
leonardo PIsano bigollo
- 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"
- He helped spread the Hindu--Arabic numerals, which is our present # system
- He was the founder of the fibonacci sequence
- He discovered this by his obsession with rabbits
Untitled Slide
- 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.
- This sequence is found in many areas of nature.
- It is a recursive function
Spirals
golden ratio
- The ratio between the numbers is 1.618034
- It is a calculation of the turns that allows the spiral to occur
- The spiral happens naturally after a new cell is formed
- These numbers all happen to be irrational numbers
Flowers
Untitled Slide
Pine Cones
Pine cones show the Fibonacci Spirals clearly. Here is a picture of an ordinary pine cone seen from its base where the stalk connects it to the tree.
Can you see the two sets of spirals?
Can you see the two sets of spirals?
Untitled Slide
Trees
You start seeing the sequence from the branches that form.
Rabbits
1.At the end of the first month, they mate, but there is still one only 1 pair.
2.At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
3.At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
4.At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
2.At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
3.At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
4.At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
Bees
You again see the sequence also in bees. A female can produce a male and a male reproduces a male and a female. Which occurs the fibonacci sequence.
conclusion
- This number sequence is in our everyday lives.
- It helps us identify the density of tree trunks, leaves, pine cones, etc.
- It also helps us understand weather and spirals.
