spirals flowing in opposite directions match neighboring sequences in Fibonacci's Sequence such as five and eight, eight and 13, or 13 and 21. Another example of the spirals that share the larger Fibonacci numbers such as 89 and 144, or 144 and 233 are flowers. The bud or seeds or a flower will grow in the same pattern as
pinecones do. Their spirals flow in opposite directions and you can count out the same idea of neighboring Fibonacci numbers in the sequence. Some popular flowers to test this theory are sunflowers or daisies. The petals that grow on roses are also capable of delivering the Fibonacci numbers to us. Some plants will even produce spirals based on how their leaves grow on their stems. Image M Fibonacci can be found in more than just the plant life or our world, though. Bees will often show us that their ancestry can produce the numbers of the Fibonacci Sequence sort of like the previously explained Rabbit Breeding theory except this time you are working backwards instead of forwards. Inside the hive is a colony of bees and you will always find your Queen Bee, your working females, and your drones which are male. Female worker bees do not produce offspring. The queen bee is the only bee in the hive to create more bees. So, let's look at how the ancestry of a bee works. The queen will be represented by ( F ) as the drone that fertilizes the egg will be known as ( M ). Our ancestry will being with a drone, the first number of Fibonacci's Sequence, one ( M ). The next branch is the queen as you wouldn't have created a drone without the queen ( M , F ). In order for the queen to have be born, she would have needed her own queen, and a drone to
fertilize the egg. That presents the third Fibonacci Sequence number of two ( M = F = M, F ). The next sequence (fourth) would be three and the ancestry does prove this because in order to have a male and female you would have needed a female to produce the male, and a set (male, female) to produce the female ( M = F = M, F = M, F, F ). The last sequence I will work to is the fifth; the previous male needed a queen, and the two females both needed a queen and a drone, leaving you with five bees ( M, M, F, F,F ). Backtracking the bee's ancestry would continue to give you the Fibonacci numbers in his sequences (1, 1, 2, 3, 5, 8, 13, 21...). Conclusion Now you will be able to spot the magic of mathematics when you are out in the world. From the birth of Leonardo Fibonacci's sequence and numbers to the Golden Ratio and Rectangle, you will forever be able recognize how this pattern has been encounter throughout history and will continue to be found in our future. The next time you find a pinecone or a nautilus shell, you'll be able to fascinate someone else's mind with the knowledge of the Fibonacci Sequence's numbers found in its growth. When viewing art or architecture, you'll have the ability to find the hidden ratio and rectangle in its aesthetically pleasing creativity or structure. You'll never be able to observe your world plainly again, as the magic of math with be surrounding you and you won't be able to help but notice it.
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- Winter '15
- Andrew Martino
- Math, Fibonacci number, Golden ratio