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Project 17 : Fibonacci Sequence

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Rakhee Mishra

 



Project 17 – Fibonacci Sequence

The Golden Thread: Exploring Fibonacci Across Subjects

The Golden Thread: Exploring Fibonacci Across Subjects

Objective:

To explore the fascinating Fibonacci sequence — its patterns in mathematics, appearances in nature, historical background, and exciting connections with other subjects like art, music, literature, and more!

🔢 Part A: Mathematical Core (20 marks)

1. Understanding the Sequence (5 marks):

  • Write the first 20 terms of the Fibonacci sequence.
  • Describe the pattern in your own words.
  • Make a colorful number chain or chart to show how it grows.

2. Fibonacci Word Problems (5 marks):

Solve 3 word problems based on the sequence. Examples:

  • A pair of rabbits gives birth every month starting from the second month. How many pairs will there be after 6 months?
  • A staircase has steps arranged in a Fibonacci pattern. How many steps will be in the 7th row?

(You may create your own problems or solve the ones given above!)

3. Ratio Exploration (5 marks):

  • Find the ratios of consecutive Fibonacci numbers (like 3/2, 5/3, 8/5...)
  • Use a calculator to write them as decimals.
  • What do you notice? What number does the ratio seem to approach?
    (Hint: It’s something called the Golden Ratio – about 1.618!)

4. Fibonacci Spiral (5 marks):

  • On graph paper, draw squares of sizes: 1, 1, 2, 3, 5, 8, 13…
  • Arrange them to form a spiral.
  • Use colors and patterns to make it beautiful.
  • Explain how the spiral is based on the Fibonacci numbers.


📜 Part B: History of Fibonacci (5 marks)

  • Who was Leonardo of Pisa, also known as Fibonacci?
  • What was the Liber Abaci and what was the famous rabbit problem?
  • Write 3 interesting facts about how numbers were used during his time.

🌱 Part C: Fibonacci in Nature (5 marks)

  • Show and explain 2 examples of how Fibonacci numbers appear in nature. Examples:
    • Number of petals on flowers
    • Leaf arrangements
    • Pinecones, pineapples, or sunflower seeds
  • Add photos, drawings, or even real leaves to support your work.


🎨 Part D: Cross-Curricular Connections (5 marks)

Choose any TWO topics from the list below and show how Fibonacci connects to them:

Option 1: Art

  • Use the Golden Ratio in your own drawing or design.
  • Research and explain how it’s used in famous paintings or architecture.

Option 2: Music

  • Find out how Fibonacci numbers or the Golden Ratio appear in musical patterns or rhythm.

Option 3: Computer Science

  • Write a simple pseudocode or draw a flowchart to show how Fibonacci numbers can be generated.
  • Explain recursion in simple words.

Option 4: Literature/Poetry

  • Write a Fibonacci poem using the syllable pattern: 1, 1, 2, 3, 5, 8
    (For example:
    I
    Am
    A fan
    Of Fib
    Nature’s pattern
    Magically spirals in all.    )

📌 How to Present Your Project:

Choose any one of the following formats:

  • A neat project file (handwritten and hand-drawn)
  • A PowerPoint presentation (maximum 12 slides)
  • A scrapbook or poster

Make sure your work is creative, neat, and original!

🧾 Assessment Criteria (Total: 50 Marks)

Section

Marks

Mathematical Exploration

20

Historical Understanding

5

Biological Applications

5

Cross-Curricular Creativity

5

Presentation & Neatness

10

Originality & Overall Effort

5

 References : 

www.gettyimages.in

www.internetsearchinc.com

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