Fibonacci and Pythagoras Unite Mathematicians, Artists, Musicians, Naturalists, Architects and Beauticians

Be the coolest one in the Math Department. Click on the picture to get your golden (and silver) ratio Fibonacci Sequence gift items. Kyle has business card cases and much, much more.

The Golden Ratio is demonstrated most simply by dividing a line segment into two unequal pieces, a big one and a small one.

If the ratio of the big piece to the small piece is the same as the ratio of the original segment to the big piece, then:  Congratulations! You have demonstrated the golden ratio!

A quick check with your super-accurate ruler will allow you to calculate that this ratio is approximately 1.6180339887-to-1.

The golden ratio has also gone by the names of the golden section, the divine proportion, the golden cut, the section, the golden number, the extreme and mean ratio, and phi.

The Pentagram is loaded with dimensions that possess the Golden Ratio. Click on the stylized Star night light by Kyle to get a pentagram of your very own.

The ancient Greeks, led by Pythagoras, recognized the importance of the golden ratio because of its many manifestations in nature, musical chords and geometric shapes, particularly the pentagram.  On an aesthetic level, the Greeks recognized that objects whose dimensions reflected the golden ratio looked more pleasing and beautiful than objects whose dimensions did not.  It is thus not just a coincidence that the most famous works of art and architecture (not only from ancient Greece but throughout history in many other cultures too) commonly have proportions that reflect the golden ratio.  The Parthenon is the most commonly cited famous example, and is loaded with golden rectangles.

While the Greeks understood the importance and aesthetics of the golden ratio, it was not until 1202 AD, when Leonardo of Pisa (a.k.a. Fibonacci) published a book called Liber Abaci, that the world understood the sequence of numbers responsible for the ratio.

These Rabbit Design pill boxes would be great Pet Med dispensers for Fibonacci and his many rabbits. Check out Kyle Design for other Fibonacci themed gifts.

In the book, Fibonacci poses a problem about a single pair of baby rabbits – a boy and a girl.   You can see where this is going already.  In the first month of life, the rabbits are too young to reproduce.  In the second month, they are still too young.  However, in the third month, the rabbits get busy and produce another pair, giving us 2 pairs of rabbits: the original old pair, and the new young pair.   In month 4, the old pair has another pair, while the young pair is too still young to copy their parents.  The rabbit count is now up to 3 pairs.   In month 5, the old pair reproduces yet again, and the young pair is now old enough to reproduce too, giving us a new total of 5 pairs.  By month 6, we have 3 mature pairs having 3 new pairs to raise our rabbit population to 8.    The sequence, as you can see by counting rabbit pairs each month is 1, 1, 2, 3, 5, 8, 13, 21, 34…   For any given month, the number of rabbit pairs you have is equal to the sum of the two previous months.   Stated more generally, any number in the sequence is equal to the sum of the previous two numbers.  Allowed to continue infinitely, (and assuming rabbit immortality) the number progression constitutes the Fibonacci Sequence.

Pythagoras might have enjoyed networking with this cool Greek Key design business card case by Kyle Design. Click on the picture to get one of your own.

Mathematicians of the day instantly recognized that as the sequence reaches infinity, the ratio of any two consecutive numbers in the sequence pencils out to be our old Greek friend, the Golden Ratio.  Ouzo and Retsina for everyone!

The Fibonacci spiral is a graphic representation of the sequence.  As the spiral passes through each successive square, the side length of that square is equal to the previous 2 squares that preceded it.

If you are looking for a great way to become a harmonic part of the whole, go to the Kyle Design website.  She has a huge number of gifts with images that are natural manifestations of the golden ratio and its beauty, including pineapple, hibiscus, sunflower,  rose design, hands, fibonacci spiral, ram, ocean waves, rabbits, human faces, strawberries, piano keyboard and music (sound vibrations), star (pentagram), seashells (nautilus), snails, just to name a few.

Pineapple lovers will enjoy these pineapple design switchplates by Kyle Design

Each of these images is available on home decor items such as switch plates, wall plates, light switch covers, ceiling fan pulls, christmas ornaments, and decorative wood jewelry boxes. They also come in personal gift items such as pill boxes, vitamin cases, eyeglass cases, hip flasks, liquor flasks, key chains, condom cases, bookmarks, money clips, and many, many more.  Many Kyle items can be personalized with engraving too!

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