Project 17 : Fibonacci Sequence

 

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.

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📜 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.

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🌱 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.

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🎨 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.)

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📌 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!

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🧾 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 : 

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