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In 1202 Leonardo of Pisa (Fibonacci) developed a recursive sequence, now called the Fibonacci Sequence. Is this sequence just a fun little mathematical trinket, or can we find it in the natural world around us?

In this lesson students will explore his famous pattern, and will use it to reveal the golden ratio, which many believe is Nature’s standard of beauty. They’ll look for evidence of the golden ratio in animals, plants, and their own bodies. Ultimately, the question becomes: do we find the ratio it because it’s there, or simply because we’re looking for it?

Students will

  • Using the ancestry of bees, generate pattern and describe a Fibonacci Number as the sum of the previous two
  • Look for occurrences of Fibonacci Numbers in nature
  • Use ratio of Fibonacci Numbers to derive golden ratio
  • Look for evidence of the golden ratio in our faces and bodies
  • Discuss whether the golden ratio is a natural phenomenon or a figment of our imagination

Before you begin

Students should be familiar with the definition of ratio, and be able to measure lengths to the nearest 0.1 cm.

Common Core Standards

Content Standards
Mathematical Practices