Fibonacci sequence

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/fibonacci-sequence

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the recurrence relation?F(n) = F(n-1) + F(n-2), with F(0)=0, F(1)=1
2. What is the primary biological application?Phyllotaxis: arrangement of plant elements (leaves, seeds, petals) in spirals
3. What is the Fibonacci sequence and how does it start?The Fibonacci sequence is a list of numbers where each number is the sum of the two before it. It starts with 0 and 1, so the first few numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and it keeps going.
4. Why do flowers and pinecones have Fibonacci numbers?Plants use Fibonacci numbers to arrange leaves, seeds, or petals in spirals that fit together tightly. This pattern gives each new leaf or seed the best chance for sunlight and space, making the plant grow efficiently.

Recurrence Relation: An equation that defines a sequence based on previous terms.
Golden Ratio (φ): An irrational number approximately equal to 1.618, derived from the ratio of consecutive Fibonacci numbers.
Phyllotaxis: The study of the arrangement of leaves, stems, and flowers on a plant.