Right next to learning your A B C’s you learn your 1 2 3’s. Both have a similarity in that they are forms of communication, but do not exist. The purpose of numbers was so that things could have meaning and value .
We have big numbers, small numbers, numbers over numbers called fractions. Numbers that are bigger than zero, numbers that are smaller than zero, numbers that go backwards known as negative numbers and ones that go forwards called positives. We can manipulate numbers with other numbers to make bigger or smaller numbers. Some numbers go forwards so impossibly forever that we can’t put a value to them, only a symbol and a name. These numbers can also go forever backwards too, represented with a dash in front of the symbol. There are imaginary numbers and a number to represent nothing.
Numbers can be used to create patterns or code to mean something. Computer language is called binary, which reads only 1’s and 0’s. Numbers can also create patterns themselves. Sequences are a set of numbers, sometimes they have a pattern and other times they do not. An arithmetic sequence is a pattern that increases or decreases steadily. 1, 3, 5, 7, 9… is an arithmetic sequence that is increasing by 2 every time. Geometric sequences have a pattern that increase or decrease by the same value but don’t necessarily increase or decrease steadily. 2, 4, 8, 16, 32… is a geometric sequence that is multiplied by 2 every time. Arithmetic and Geometric sequences are fairly common and easy to grasp. Other common patterns are square and cube patterns (1, 4, 9, 16, 25… and 1, 8, 27, 64, 125…), which are just patterns in the numbers. Some patterns incorporate numbers and pictures.
One of the most common number patterns is known as the Fibonacci sequence. Fibonacci’s sequence goes 1, 1, 2, 3, 5, 8, 13, 21… Do you see the pattern? It’s a little trickier than the others but still quite simple. You get Fibonacci’s number by adding the first two numbers to get the next one (1+1=2, 1+2=3, 2+3=5, 3+5=8…). Is there significance in this pattern, or is it just a cool pattern? The answers can found in nature. (http://en.wikipedia.org/wiki/Fibonacci_number)
Start by dividing one number in the fibonacci sequence by the number before it. (3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615…) Notice how all the numbers start getting closer and closer together towards the same number 1.618? Much like Pi which written shorthand as 3.14, Phi is written shorthanded as 1.618, (although both are irrational and can’t be written out completely in decimal form because they lack an end). Phi is known as the golden number. The significance of this number is that it is an irrational number. Because of the irrationality of phi, it can’t be written as a fraction which is what makes them vital for plants in nature.
Sunflowers are the easiest to see Fibonacci numbers in. Plants take in light from the sun which means in order to be a good plant and survive, you need to show as much “skin” (leaves/seeds/petals) as you can without overlaps and gaps. The center of sunflowers grow their seeds in a spirally kind of pattern. These seeds rotate from the next at 61.8% (Phi!) of a full rotation, (or about 222.5 degrees). This angle of rotation gives planets the optimal conditions to fit the most seeds in the smallest area possible with the smallest amount of gaps. If one was to take the time to count the seed in a spiral the Fibonacci numbers would appear again, 34 seeds counterclockwise and 55 seeds clockwise. (http://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html) But sunflowers aren’t the only plants to have Fibonacci numbers. Other plants have it; pinecones, pineapples, cauliflower/broccoli tops, are a few examples.
The Fibonacci sequence has both significance and is cool. Some people however have a hard time accepting both facts. Some say nothing has the golden ratio in it, and that it doesn’t exist. Others believe in it so strongly they claim it to be in places it is not. The second group claim the golden ratio/spiral in; nature, nautilus shells, galaxy spirals, hurricane arms, ocean waves, famous paintings (such as the Mona Lisa), The Parthenon, and the ideal human face. These are just a few examples of what they claim to be “golden” items, but not all are. While nature does indeed have the ratio, not everything does, nautilus shells do have aspects of the ratio, but are not how they claim it to be. The case is the same with the Parthenon. Famous paintings such as Da Vinci’s “Last Supper” and “The Annunciation” do indeed have the golden ratio, but not all paintings do. (http://www.goldennumber.net/golden-ratio-myth/)
As for the ideal human face the myths and the facts are harder to distinguish. The idea isn’t does the human face have the golden ratio in it. The idea is, will an ideal (perfect/attractive) face be made of the ratio. Tons of research has be done to both prove and disprove it, but more evidence suggests that an ideal face will have the golden ratio. Would this suggest that the human mind favors the ratio? Is our mind pre programmed to favor items with the ratio? If so then the mind would favor a form of order in an unorganized (irrational) number. I would think that irrational numbers would make anyone cringe to look at (Or at least I do, and I know I can’t be the only one). There’s no end to them, and they can’t be put into a nice even fraction. That instantly makes them not nice. So why would the mind favor a ratio that is irrational?
In my 9th grade science class we were all required to do a science fair project. I ended up doing mine on soundwaves and when directed at a curve can be heard great distances away despite the volume of the sound. Some friends of mine did theirs on Phi. They wanted to see whether people would favor items in a room that were of the golden ratio versus those that were not. They drew two rooms in a one point perspective, one with Phi the other just slightly off. They would ask people which room they liked more. Next they drew different forms of furniture (couches, tables, chairs, wardrobes) in the same manner. One being Phi the other just a little off, and asked everyone individually which they liked more. What they found was that more people favored the room and items that were the golden ratio over those that were not.
Keep in mind this was an experiment done by high school students in 9th grade, that does not make it an a perfect experiment. But it is an interesting idea to ponder upon.