The Golden Ratio Activities

1. Magic trick to start the unit. Have students chose an two integer numbers (preferably less than 10). Using these two numbers as the first two in a sequence, generate the next terms by finding the sum of the previous two. Extend this sequence to more than 10-11 terms. Then find the ratio of “larger/smaller.” The ratios will all converge to 1.618, The Golden Ratio.
2. Read “Gold Finger,” a chapter from Here’s Looking at Euclid by Alex Bellos (2011).
3. Using compass and straightedge, construct a golden segment (can extend to a golden rectangle)
4. Art….use the golden segment created using compass and straightedge to create an art piece. Include an explanation of how the segments are used in the drawing.
5. Find some everyday objects and measure them to see how close they are to the Golden Ratio.
6. Derive Phi and see WHY it is approximately 1.618.
7. Watch Vi Hart’s series of videos on Fibonacci Numbers and spirals

Here is a link to The_Golden_Ratio_Packet_of_Gold_Fall_2014

Here is a link to a Golden Ratio Video Math_Art_Tech_Hist_Golden_Ratio Project Rubric Fall 13

8. Students create their own “mathematically correct flower,” by using an angle-0-tron and layering petals of a flower, each a golden angle apart.
9. Create a Golden Ratio video through Movie Maker that includes a summary of the Golden Ratio in your own words, an art piece with explanation, two photographs that you took that illustrate a connection to the Golden Ratio, and at least one measurement to test for the Golden Ratio.
9. Use glitter glue to find the number of spirals in pinecones.

Student Work: