## Learning Objects (7)

### Direct Access Links:

**The Magic of Fibonacci Numbers | Arthur Benjamin (TED)**

**Fibonacci Everywhere (Smithsonian)**

**Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3] (Vihart)**

**The Golden Ratio (National Geographic)**

**Drawing the Golden Ratio – Beginners**

**The BBC on the Fibonacci Sequence (BBC)**

**Fibonacci-Sequence-in-Nature (Fourth Grade Lesson University of Hawaii)**

## Overview

Named after a 13th century Italian Mathematician, Leonardo of Pisa, each number in the Fibonacci sequence is created by adding the previous two together. It starts 1 1 2 3 5 8 13 21 and goes on infinitely. In makes an appearance time and again in the natural world, from the spirals on a pinecone to the petals on a sunflower. The Fibonacci sequence is also the mathematical first cousin of the Golden Ratio – a number that has haunted human culture for thousands of years and who some believe is the essence of beauty. It’s found in the proportions of the Parthenon and the paintings of Leonardo Da Vinci. It even made a cameo appearance in “The Da Vinci Code.” While trying to decipher the clues left at the murder scene in the Louvre that opens the novel, the hero, Robert Langdon, “felt himself suddenly reeling back to Harvard, standing in front of his ‘Symbolism in Art’ class, writing his favorite number on the chalkboard. 1.618.”

**The Magic of Fibonacci Numbers | Arthur Benjamin**

Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

### Fibonacci Everywhere

“Fibonacci retracement” is a tool that technical analysts use to guide their outlook about buying and selling behavior in markets. This technique is named after and derived from the famous Fibonacci sequence, a set of numbers with properties related to many natural phenomena. While using these numbers to predict market movements is a lot less certain than using it to calculate sunflower seed patterns, the appearance of the sequence in the field of finance is yet another testament to its power in capturing the human imagination.

### Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]

Watch this set of three videos as Vi Hart describes through spirals on her doodle pad how the Fibonacci Sequence can be found throughout nature, in geometric shapes and more.

### The Golden Ratio

The “golden ratio” is a unique mathematical relationship. Two numbers are in the golden ratio if the ratio of the sum of the numbers (a+b) divided by the larger number (a) is equal to the ratio of the larger number divided by the smaller number (a/b). The golden ratio is best approximated by the famous “Fibonacci numbers.”

### Drawing the Golden Ratio – Beginners

Learn how to create pleasing images and logos using the Golden Ratio. Circles and other shapes are explained along with computer tips for creating a logo.

### The BBC on the Fibonacci Sequence

Melvyn Bragg discusses the Fibonacci Sequence with guests including: Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Jackie Stedall, Junior Research Fellow in History of Mathematics at Queen’s College, Oxford; Ron Knott, Visiting Fellow in the Department of Mathematics at the University of Surrey.

### Fibonacci-Sequence-in-Nature

### Elementary Lesson – 4th Lesson

Nature is all about math. If you were to observe the way a plant grows new leaves, stems, and petals, you would notice that it grows in a pattern following the Fibonacci sequence. Plants do not realize that their growth follows this sequence. Rather, plants grow in the most efficient way possible – new leaves and petals naturally grow in spaces between old leaves, but there is always enough room left for one more leaf or petal to grow.

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### Pedagogy

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