HoneybeesĪ honeybee colony consists of a queen, a few drones and lots of workers. For example, lilies and irises have three petals, buttercups and wild roses have five, delphiniums have eight petals and so on. This pattern continues, following the Fibonacci numbers.Īdditionally, if you count the number of petals on a flower, you'll often find the total to be one of the numbers in the Fibonacci sequence.
Then the trunk and the first branch produce two more growth points, bringing the total to five. The main trunk then produces another branch, resulting in three growth points. One trunk grows until it produces a branch, resulting in two growth points. Some plants express the Fibonacci sequence in their growth points, the places where tree branches form or split. You can decipher spiral patterns in pine cones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner. Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. Amazingly, if you count these spirals, your total will be a Fibonacci number. Look at the array of seeds in the center of a sunflower and you'll notice they look like a golden spiral pattern. Here are a few examples: Seed Heads, Pinecones, Fruits and Vegetables You can commonly spot these by studying the manner in which various plants grow. Make sure to watch the video for a visual explanation and more information about the awesome power of the golden ratio-and why it is the most irrational of numbers.But while some would argue that the prevalence of successive Fibonacci numbers in nature are exaggerated, they appear often enough to prove that they reflect some naturally occurring patterns. As the video demonstrates, this is because the golden ratio is a highly irrational number, meaning it is not very well approximated by any whole number or even any fraction of whole numbers.Īs it turns out, when you map the seeds of a sunflower on the face of the flower, it's as though the flower were playing this very game, placing seeds to near mathematical perfection. The best number to rotate the flower for optimal seed placement is the golden ratio, where the entire face gets covered more or less evenly without the seeds clustering in any one spot. If you do 1/3 of a turn then you will get 3 lines of seeds, and if you do 1/10 of a turn you get 10 lines. If you place a seed, and then rotate the flower face a certain amount, and place another seed, and then repeat this process, what would be the ideal amount to rotate the flower face?įor example, if you place a seed, rotate the flower 1/2 turn, place another seed and repeat, then you will get two parts of the flower with all the seeds. The idea is that you have a flower, and you are trying to place seeds on the face of the flower in such a way that you can fit as many as possible. (If you take the shorter length of a golden rectangle and make a square with that length, and then remove the area of that square from the golden rectangle, you are left with another, smaller golden rectangle.)Ī mathematical method for exploring irrational numbers is to play a kind of game. In geometry, this number produces some fascinating patterns, such as a golden rectangle.
#Golden ratio numbers plus
The wonderful YouTube channel Numberphile recently spoke to Ben Sparks, a mathematician working at the University of Bath, to reveal the true nature of the golden ratio: 1 plus the square root of 5 over 2, or approximately 1.62, represented in mathematics by the Greek letter phi. These claims are rough approximations of the golden ratio at best and pseudoscience at worst.
Others have said that the most beautiful people are those with features aligned according to the golden ratio. For example, many claim the ancient Greek Parthenon has numerous examples of the golden ratio in its design. The golden ratio is an almost mythical number that you may have heard of in various areas of architecture or design.
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