2. GOLDEN RATIO

3. GOLDEN SECTION

4. FIBONACCI NUMBERS 1, 1, 2, 3, 5, 8, 13….. The ratio of any consecutive numbers is the golden ratio A pattern found in nature all the time Mating habits of bees Number of flower petals on a flower Golden Rectangle Made by grouping squares that measure with lengths of Fibonacci numbers The spiral made is found in nature

5. GOLDEN SPIRAL

6. MODERN USES

7. TWITTER

8. WHERE IS IT FOUND? Leonardo da Vinci

9. Leonardo's famous Mona Lisa reflects the artist’s use of the Golden Section. * The rectangle around her face represents a Golden rectangle. * If you subdivide the rectangle at the eyes the vertical side of the rectangle is divided by the golden ratio.

10. Even in the time of the ancient Greeks, the golden rectangle was considered a pleasing shape. It appears in many of the proportions of the Parthenon in Athens, Greece.

11. GOLDEN RATIO IN HUMAN HAND AND ARM Look at your own hand The length of different parts in your arm also fits the golden ratio.

12. MUSIC On a piano: There are 13 of each note A scale has 8 notes The 5 th and 3 rd notes are considered the foundation of all chords This follows the Fibonacci Sequence Parts of a musical work: the big “hit” of a piece of music is approximately.618 of the way though a piece of music

13. GOLDEN RATIO AND THE FACE The ratio of different parts of your face (ideally) meet the golden ratio. Directions: Measure your partner’s face and then plot the ratios on our class histogram. Record these histograms on your sheet