Math+in+Nature+Flora+K

=** Math in Nature **= = =

=FIBONACCI NUMBER IN NATURE= Fibonacci is a name for a sequence of numbers. Fibonacci number look like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,....... The first two numbers of the Fibonacci number is 0 and 1 by definition. The rest of the numbers are obtained by adding the two previous numbers (0+1= 1, 1+1= 2, 1+2= 3,.....). Fibonacci numbers may also go down to negative numbers but they are not shown on many sources. Fibonacci numbers can be used to make a spiral, and this spiral is called the Fibonacci Spiral. Believe it or not, this spiral can be seen being used in the nature!! In snail shells, pine-cone, pineapple, etc.

HOW TO DRAW FIBONACCI SPIRAL:
1. On a graph paper, draw 2 squares (1x1) side to side <- this makes a 2x1 rectangle. 2. On top of the rectangle, draw another square (but this time, 2x2) <- this makes a 2x3 rectangle 3. On the right side of the rectangle, draw a 3 by 3 square <- This makes a 5x3 rectangle 4. On bottom of the rectangle, draw a 5 by 5 square <- This makes a 5x8 rectangle 5. On the left side of the rectangle draw an 8 by 8 square <- This makes a 13x8 rectangle 6. On top of the 13x8 rectangle, draw a 13 by 13 square

Up to this step, you've created a Fibonacci rectangle!! But that's not what we're trying to draw here. To transform Fibonacci rectangle into a Fibonacci spiral, we have to draw some curves...

7. Start with the one of the 1x1 squares (one on the right). 8. Connect 2 opposite corners (top right and bottom left) of the square with a curve. 9. For the second square (1x1), again connect 2 opposite corners, starting with the corner that you ended with before (bottom left of first square). 10. Continue on like this, and you will end up with the Fibonacci Spiral!! :D

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Fibonacci spirals are quite similar looking to the Golden Spiral, which are drawn using the golden section. This is because the Fibonacci Spiral approximates the golden spiral. It is the proportion that is known to be most visually pleasing to the eye. (Golden section is known to be the proportion that is most visually pleasing to the eye. Is this why nature is so visually pleasing??) Fibonacci Spiral Golden Spiral

Here are some things in nature that have Fibonacci spirals:
Snail Shells

Flowers

Pine-cones

Galaxy Hurricanes

=SYMMETRY IN NATURE= As wells as Fibonacci Number, Symmetry can also be seen in nature. Symmetry is defined as the exact correspondence of form and constituent configuration on opposite sides of a dividing line, plane or about a center or an axis. In other words, symmetry means something is exactly corresponding in shape and size to its opposite side when divided. However in nature, things may not be PERFECTLY symmetrical, buy are most of the ALMOST perfectly symmetrical. Symmetry also reflects beauty and perfection, being visually pleasing to the eye (woah, nature has everything that represents beauty o__o Humans are also symmetrical by the way,,,,;;).



Here are some things in nature that are symmetrical:
Butterflies Cats Starfish Peacocks Flowers

CITATION:
 * companies)., auto insurance. "Shallow Thoughts." The Shallow Sky. N.p., n.d. Web. 16 Jan. 2010. .
 * "Jencropable » Blog Archive » The Fibonacci Spiral." Jencropable . N.p., n.d. Web. 16 Jan. 2010. .
 * However, two knuckles. All of these numbers fit into the sequence.. "Fibonacci Numbers and Nature." Jim Wilson's Home Page. N.p., n.d. Web. 16 Jan. 2010. .
 * "Mathematical paintings and sculptures: Fibonacci spiral in nature." Mathematical paintings and sculptures. N.p., n.d. Web. 16 Jan. 2010. .
 * definition, the first two Fibonacci numbers are 0, 1, each remaining number is the sum of the previous two. Some sources omit the initial 0, and instead beginning the sequence with two 1s.. "Fibonacci number - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 16 Jan. 2010. .
 * "Golden ratio - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 16 Jan. 2010. .
 * " Symmetry Definition | Definition of Symmetry at Dictionary.com." Dictionary.com | Find the Meanings and Definitions of Words at Dictionary.com. N.p., n.d. Web. 16 Jan. 2010. .
 * "Symmetry - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 16 Jan. 2010. .
 * Abney, Angel, and Andy Tyminski. "Symmetry in Nature." Jim Wilson's Home Page. N.p., n.d. Web. 16 Jan. 2010. .
 * "Mathematics in Everyday Life." Mathematics in Everyday Life. N.p., n.d. Web. 16 Jan. 2010. .
 * " EyeFetch Photography - Symmetry on Concrete by serendipitytoni." EyeFetch.com - Digital Art & Photography Community. N.p., n.d. Web. 16 Jan. 2010. .
 * "Sexual Paradox: Chaos." Dhushara. N.p., n.d. Web. 16 Jan. 2010. .
 * "Cat Symmetry on Flickr - Photo Sharing!." Welcome to Flickr - Photo Sharing. N.p., n.d. Web. 16 Jan. 2010. .