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#Series and sequences math and science initiative how to#
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8.1: Sequences We commonly refer to a set of events that occur one after the other as a sequence of events.

"It's all just wishful thinking."Įditor's note: Adam Mann contributed to this article.\) We can see a pattern regardless of whether it's there or not," Devlin said. All these claims, when they're tested, are measurably false, he added. Overarching claims about the ratio being "uniquely pleasing" to the human eye have been stated uncritically, Devlin said. Since then, people have said the golden ratio can be found in the dimensions of the Pyramid at Giza, the Parthenon, Leonardo da Vinci's "Vitruvian Man" and a bevy of Renaissance buildings.

In subsequent years, the golden ratio sprouted "golden rectangles," "golden triangles" and all sorts of theories about where these iconic dimensions crop up. Much of this misinformation can be attributed to an 1855 book by the German psychologist Adolf Zeising called "Aesthetic Research." Zeising claimed the proportions of the human body were based on the golden ratio. "It would take a large book to document all the misinformation about the golden ratio, much of which is simply the repetition of the same errors by different authors," George Markowsky, a mathematician who was then at the University of Maine, wrote in a 1992 paper in the College Mathematics Journal. When people start to draw connections to the human body, art and architecture, links to the Fibonacci sequence go from tenuous to downright fictional.

Perhaps the most famous example of all, the seashell known as the nautilus, does not in fact grow new cells according to the Fibonacci sequence, he added. Are there real-life examples of the Fibonacci sequence? "It's not 'God's only rule' for growing things, let's put it that way," Devlin said. But there are just as many plants that do not follow this rule. Pinecones exhibit a golden spiral, as do the seeds in a sunflower, according to " Phyllotaxis: A Systemic Study in Plant Morphogenesis" (Cambridge University Press, 1994). For instance, the spiral arrangement of leaves or petals on some plants follows the golden ratio. The golden ratio manages to capture some types of plant growth, Devlin said. Read more: The 9 most massive numbers in existence The ratio of successive numbers in the Fibonacci sequence gets ever closer to the golden ratio, which is 1.6180339887498948482. It's true that the Fibonacci sequence is tightly connected to what's now known as the golden ratio, phi, an irrational number that has a great deal of its own dubious lore.

#Series and sequences math and science initiative code#

However, it's not some secret code that governs the architecture of the universe, Devlin said. Other than being a neat teaching tool, the Fibonacci sequence shows up in a few places in nature. (Image credit: Shutterstock) Why is the Fibonacci sequence important? The Fibonacci sequence and the golden ratio are eloquent equations, but they aren't as magical as they may seem. In 1877, French mathematician Édouard Lucas officially named the rabbit problem "the Fibonacci sequence," Devlin said. In fact, it was mostly forgotten until the 19th century, when mathematicians worked out more about the sequence's mathematical properties. But after a few scant paragraphs on breeding rabbits, Leonardo of Pisa never mentioned the sequence again. "Liber Abaci" first introduced the sequence to the Western world. Read more: 9 equations that changed the world The answer, it turns out, is 144 - and the formula used to get to that answer is what's now known as the Fibonacci sequence. (Ignore the wildly improbable biology here.) After a year, how many rabbits would you have? A month later, those rabbits reproduce and out comes - you guessed it - another male and female, who also can mate after a month. After a month, they mature and produce a litter with another male and female rabbit. The problem goes as follows: Start with a male and a female rabbit. In one place in the book, Leonardo of Pisa introduces the sequence with a problem involving rabbits. Written for tradesmen, "Liber Abaci" laid out Hindu-Arabic arithmetic useful for tracking profits, losses, remaining loan balances and so on, he added.

#Series and sequences math and science initiative how to#

However, in 1202 Leonardo of Pisa published the massive tome "Liber Abaci," a mathematics "cookbook for how to do calculations," Devlin said. (Image credit: Stefano Bianchetti/Corbis via Getty Images) However, in 1202 in a massive tome, he introduces the sequence with a problem involving rabbits. Portrait of Leonardo Fibonacci, who was thought to have discovered the famous Fibonacci sequence.