The Golden Ratio Math in Beauty, Art, and Architecture Adapted from Ms. Stanley’s presentation: http://stanleyprealgebra.wikispaces.com

AIM: What is the Golden Ratio? Do Now: Write the following ratio five different ways: 14: 36

BIG IDEAS The Golden Ratio is represented by the Greek letter “phi” - φ This is the Golden Ratio

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa aka "Fibonacci" and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. —Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number

Now, we’re going to examine the BEAUTY of the Golden Ratio This is Leonardo da Vinci's example of “Divine Proportions” from De Divina Proportione (On the Divine Proportion) He believed that beauty was direectly related to the Golden Ratio If a person’s face was proportionate, according to the Golden Ratio, they would be more beautiful, he believed. Do you think that could be true?

Is Jessica Simpson Beautiful?

Would Leonardo Da Vinci think she was pretty? By comparing the length of her face to the width of her face, you get the Golden Ratio!  

What is the Golden Ratio? The Golden Ratio is... 1.6180339887... Is it rational or irrational?

A Simple Example of the Golden Ratio The Golden Rectangle The ratio of the long side of the triangle to the short side of the triangle is the golden ratio. Short Side: 1 unit Long Side: 1.618... units Phi represents the Golden Ratio.

Where can we find the Golden Ratio? ART The Mona Lisa by Leonardo Da Vinci If you draw a rectangle around Mona Lisa's face, the dimensions of the rectangle form the golden ratio.  

Where can we find the Golden Ratio? Architecture The Parthenon Ancient Greek Temple Built in 5th Century BC    If you compare the length and width of the Parthenon you get the Golden Ratio. The Parthenon has more than just one Golden Ratio.

Where can we find the Golden Ratio? New York City The United Nations building is located on 42nd Street and FDR Drive. The width of the building compared to the height of 10 floors is the Golden Ratio.  

Project Time: You will now see if different famous people are beautiful according to Leonardo da Vinci You will be assigned one famous person Using the provided ruler, you will complete the handout The handout will help you figure out if Leonardo da Vinci would think these people are beautiful! You will begin the project today and complete it by the end of tomorrow.

Where can we find the Golden Ratio? Your Body! The length of your forearm compared to the length of your hand is the Golden Ratio. Also the height of your body compared to the height of your belly button is the golden ratio. Do your forearm and hand form the golden ratio?

The Golden Ratio and the Math Expo AIM: Finding the Golden Ratio in Faces and picking projects for the Math Expo. DO NOW: What is the Golden Ratio (as a number)?  Give one example of where you can find the Golden Ratio.