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November 23, 2016

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Happy Fibonacci Day! This day, November 23, recognizes the importance of the Fibonacci sequence (or Fibonacci numbers) in mathematics and our everyday lives. Here are 7 fun facts that will entertain and educate your class about how this mathematically awesome theory relates to—and can be seen in—our everyday lives.

**1. What is the Fibonacci sequence?**

This is a pattern of counting where each number is the sum of the previous two. (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … and so on.) The sequence shows that the sum of any two consecutive numbers equals the next number. After the first four numbers, the ratio of any number to its next highest number approaches 0.618. The ratio of alternate numbers approach .382. These ratios are often simplified to the key Fibonacci levels: 38%, 50%, and 62%.

**2. Fun with Fibonacci numbers**

Check out this inspiring Ted Talk: mathemagician Arthur Benjamin explores the magic of the weird and wonderful Fibonacci sequence. Benjamin shows how Fibonacci numbers are added and subtracted to create rectangles and spirals, and the beauty in the world around us.

**3. Who discovered the Fibonacci sequence?**

Leonardo Bonacci, also known as “Fibonacci” and “Leonardo of Pisa,” was a highly regarded Italian mathematician in the Middle Ages. This master mathematician discovered the Fibonacci sequence, still used today in business, computer data storage and processing, as well as seen in the world around us. He introduced Fibonacci numbers in his book published in 1202, *Liber Abaci.* This ground-breaking book also introduced to the Western World the Hindu-Arabic numeral system we use today (1, 2, 3), replacing the use of Roman numerals (I, II, III), and the abacus for calculations.

**4. How are Fibonacci numbers used in today’s business world?**

This sequence is heavily used in the trading of stocks to measure trend changes and price targets. Stock traders frequently look to the “Fibonacci retracement” when predicting future share prices. The Fibonacci sequence is also used in computer data storage and processing.

**5. Fibonacci numbers and the Golden Ratio**

The Golden Ratio is closely related to and symbolized by Phi which is the ratio of the circumference of a circle to its diameter. (Phi goes on infinitely but is rounded off to 1.618.) Interestingly, there’s a naturally occurring relationship between the Golden Ratio and Fibonacci numbers: The ratio of any two successive Fibonacci numbers is very close to the Golden Ratio. This relationship is used to explain the naturally occurring rectangles and spirals in plants, flowers, and seashells, and it has also been used to create shapes in architecture and art as far back as the great pyramids of ancient Egypt.

**6. The Fibonacci sequence in architecture**

The Fibonacci sequence can be seen everywhere: in art, architecture, and nature. The Fibonacci Terrace at the Science Centre in Singapore is just one example: Tiles are arranged to form shapes with sides in proportion to Fibonacci numbers. Here’s what it looks like:

**7. The Fibonacci sequence in nature**

Even if you didn’t know its name, you’ve probably seen the Fibonacci sequence while walking through the forest or digging your toes into the sand at the beach. It’s all over—in sunflowers, seashells, unfurling ferns, and pine cones to name just a few. Even if the mathematical proof of this sequence of numbers is a little advanced, here’s a short video that does a great job of showing examples from nature.

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