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Grade 5-6

Golden Spiral: What is the Fibonacci Sequence and the Golden Ratio?

by Ariella F. | Math

4 Lessons 58:04
  1. 1. Fibonacci Sequence and Rabbits 9:51
  2. 2. The Golden Spiral 19:45
  3. 3. The Golden Rectangle 16:29
  4. 4. Let’s Bring It All Together 11:59

Grade 5-6



What is the golden spiral? Fibonacci sequence? Golden ratio? Have you ever held a seashell up to your ear to hear the ocean? If you look closely at the shell you will notice a spiral; this is not unique to seashells as this pattern frequently occurs in nature. To understand the spirals that occur in sunflowers, pineapples, and the Mona Lisa we must look into the work of Fibonacci, an Italian mathematician. We will also uncover the mathematical constant phi, otherwise known as the golden ratio, by observing nature, architectural works, and art pieces. Finally, we will derive phi’s close relationship to the Fibonacci sequence. After completing this course it will be impossible to ignore the golden spiral in your everyday life!


  • Art
  • Fibonacci Sequence
  • Golden Ratio
  • Golden Rectangle
  • Golden Spiral
  • Nature


I’m a sophomore Economics major at Barnard College. I previously attended Montclair High School and have been tutoring for six years. I have done private tutoring as well as Barnard Peer-to-Peer tutoring. I am organized and creative, so I can consistently think of new ways to explain the material. I also am approachable and encouraging, so students will feel comfortable interacting with me. I begin my tutoring sessions gathering the problems the student had the greatest difficulty with and after reviewing these I create practice exams from a mix of their past problem sets, problems I find online, and problems I make up to target specific areas the student is struggling with.

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