Fibonacci Sequence Project Ideas for Science Fair

The Fibonacci Sequence is a fascinating numerical pattern where each number is the sum of the two preceding ones. Found in nature, art, and mathematics, it offers a unique perspective on growth and structure. Here are three engaging examples of exploring the Fibonacci sequence that can serve as exciting science fair projects.

Example 1: Fibonacci in Nature

Context

The Fibonacci sequence is prominent in nature, particularly in the arrangement of leaves, flowers, and even animal reproduction. This project involves investigating how the Fibonacci numbers manifest in various biological systems.

To conduct this study, students can collect data from local plants or flowers and analyze their structures based on Fibonacci numbers. For instance, they can observe the number of petals on flowers or the arrangement of seeds in a sunflower.

Example

1. Select several plants or flowers: Choose at least five different species that are known to exhibit Fibonacci numbers. Common examples include sunflowers (34 or 55 seeds), lilies (3 petals), or daisies (34 or 55 petals).
2. Document your findings: Count the number of petals or the arrangement of leaves on each plant. Use a notebook or digital spreadsheet to record your data.
3. Analyze the results: Create charts or graphs to visually represent your findings. Highlight the most common Fibonacci numbers observed among the plants studied.

Notes and Variations

• Consider photographing the plants and including visuals in your presentation.
• Explore the mathematical ratios related to Fibonacci numbers, such as the Golden Ratio (approximately 1.618), which is often associated with these patterns.

Example 2: Fibonacci Spiral Art

Context

The Fibonacci sequence is not only mathematical but also artistic. This project invites students to create art using Fibonacci spirals, demonstrating how math can inspire creativity.

Example

1. Materials needed: Graph paper, a ruler, a compass, colored pencils, or markers.
2. Draw the Fibonacci Sequence: Start by drawing squares with side lengths corresponding to Fibonacci numbers (1, 1, 2, 3, 5, 8, etc.). Begin with two 1x1 squares, then continue the sequence by adding squares of size 2, 3, 5, and so on.
3. Create the Spiral: Use the compass to create quarter circles that connect the corners of the squares, forming a spiral.
4. Color Your Spiral: Use colored pencils or markers to fill in the squares or enhance the spiral with patterns.

Notes and Variations

• Explore the concept of the Golden Ratio by measuring the ratios of the sides of the squares created.
• Consider creating a digital version of your spiral using graphic design software for a modern twist.

Example 3: Fibonacci Sequence in Computer Programming

Context

The Fibonacci sequence is a classic example in computer science and programming. This project involves writing a simple program to generate Fibonacci numbers and exploring their applications in algorithms.

Example

1. Select a programming language: Choose a language you are familiar with, such as Python, Java, or JavaScript.
2. Write the Fibonacci Generator: Create a function that generates Fibonacci numbers. Below is a sample code in Python:

   def fibonacci(n):
       fib_sequence = [0, 1]
       while len(fib_sequence) < n:
           next_fib = fib_sequence[-1] + fib_sequence[-2]
           fib_sequence.append(next_fib)
       return fib_sequence

#   # Generate the first 10 Fibonacci numbers
   print(fibonacci(10))  # Output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

3. Experiment with variations: Modify the program to generate Fibonacci numbers in different formats, such as lists or graphical representations.
4. Application of Fibonacci in programming: Research how Fibonacci numbers are used in algorithms, such as sorting or searching, and present your findings.

Notes and Variations

• Include a visual representation of the Fibonacci sequence using a graphing library, such as Matplotlib in Python.
• Explore the concept of recursion by writing a recursive function to generate Fibonacci numbers and compare its efficiency with the iterative version.

These projects not only enhance understanding of the Fibonacci sequence but also encourage creativity and critical thinking. Engaging with these examples will provide insights into the mathematical beauty and practical applications of this intriguing sequence.