1. Vitruvian Man Golden Ratio Da Vinci’s drawing of the Vitruvian Man

2. The Vitruvian Man was a drawing by Leonardo Da Vinci. The Golden Ratio was first defined in Euclid’s book Elements. It is defined as “"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Vitruvian Man & Golden Ratio

3. About Da Vinci Born in Vinci, Italy on April 15, 1452 Died on May 2, 1519 at age 67 His most famous work is the Mona Lisa (pictured below) He was a painter, sculptor, architect, musician, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer.

4. The Golden Ratio It is represented by the Greek lowercase letter phi (φ) It is said to be very aesthetically pleasing It is approximately 1.61803 It is widely used in both math, art, and even music

5. The Vitruvian Man The drawing is based on the ideal human proportions described by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura. Other artists tried to depict this concept but didn’t succeed. This picture was part of Da Vinci’s attempts to relate man to nature.

6. Examples of the Golden Ratio

7. Steps to create Vitruvian Man Proportions Step 1: Draw a square and circle (radius R1) as shown below Step 2: Move circle so point A overlaps with point B (see below) Step 3: Locate center of the final circle (point O) by Dividing distance AB in a half. Draw new circle with radius R2=OA (see below)

8. Steps to create Vitruvian Man Proportions – Part 2 Finished! The result matches perfectly Leonardo's drawing

9. “From sculptures, paintings, sketches, buildings, monuments, to mathematics- everything can be connected to this magnificent ratio. Leonardo Di Vinci found importance in it, as seen evident in his paintings. Composers produced their music to the length and timing of this Ratio or Section. Nature grows in accordance to this. This is a universal equation to help describe, mathematically, why we like the things we do.” (Da Vinci – Golden Ratio)

10. Credits - Webpages http://www.personal.psu.edu/ztr102/goldenrat io.html (Da Vinci - Golden Ratio) http://www.personal.psu.edu/ztr102/goldenrat io.html http://www.world- mysteries.com/sci_17_vm.htm http://www.world- mysteries.com/sci_17_vm.htm http://en.wikipedia.org/wiki/Leonardo_da_Vin ci http://en.wikipedia.org/wiki/Leonardo_da_Vin ci

11. Credits - Images http://en.wikipedia.org/wiki/Golden_ratio http://www.goldennumber.net/golden-section/ http://zissou.com/2011/04/07/the-golden- ratio/ http://zissou.com/2011/04/07/the-golden- ratio/ http://designorz.wordpress.com/2012/08/01/m aths-and-design/ http://designorz.wordpress.com/2012/08/01/m aths-and-design/ http://www.leonardo.net/main.html http://www.world- mysteries.com/sci_17_vm.htm http://www.world- mysteries.com/sci_17_vm.htm