This Weird Little Number Pattern Can Power Your Next Science Fair Project

Why does this strange sequence show up everywhere?

Let’s start with the pattern itself, but in a very human way.

The Fibonacci sequence goes:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each number is the sum of the two before it. That’s it. No magic. No secret formula (well, there is a fancy formula, but you don’t need it for a science fair project unless you really want to flex).

So why do people get so excited about it? Because once you notice it, you start seeing it everywhere. Not in some mystical “the universe is sending me a sign” way, but in a very practical, biological, and geometric way.

Think about this:

• The way sunflower seeds spiral
• The layout of pinecone scales
• The way some plants arrange leaves around a stem

Again and again, the counts and angles match Fibonacci numbers or ratios related to them. That’s where your science fair project can move from “cool pattern” to “actual investigation.”

Turning Fibonacci into a real science fair question

Science fair judges don’t just want “cool facts.” They want a question, a method, and a conclusion. So instead of “The Fibonacci Sequence in Nature,” try something more like:

• How often do Fibonacci numbers appear in common plants I can find locally?
• Does the Fibonacci sequence help plants pack seeds more efficiently?
• Can Fibonacci-based spirals reduce wasted space compared to other patterns?
• Can a simple Fibonacci model predict population growth better than linear growth?

Notice the pattern? You’re not just describing; you’re testing or comparing.

Let’s break down a few project directions you can actually build, step by step.

Project path 1: Fibonacci in plants you can hold in your hand

Imagine Mia, 8th grade. She’s not trying to win the International Science and Engineering Fair. She just doesn’t want another boring poster. She decides to investigate whether Fibonacci numbers really show up in everyday plants from her yard and the grocery store.

Her core question becomes:

Do Fibonacci numbers appear in the leaf, petal, or seed patterns of common plants around me?

How to collect your “nature data”

You don’t need a rainforest. You can use:

• Pinecones
• Sunflowers (whole heads are great)
• Daisies or similar flowers
• Succulents
• Broccoli or Romanesco (if your store sells it)

For each plant, you can:

• Count petals (a lot of flowers have 3, 5, 8, 13, or 21 petals)
• Count spiral rows on pinecones and sunflowers (clockwise and counterclockwise)
• Note leaf arrangements around the stem

You then compare your counts to Fibonacci numbers. How often do they match? When they don’t match, what happens instead?

Making it feel like real science, not just a scavenger hunt

To move this from “fun counting” to a real project, you can:

• Decide ahead of time how many plant samples you’ll collect (for example, 20–30 different flowers or cones)
• Keep a data table with columns like: Plant type, Petal count, Fibonacci? (Y/N)
• Calculate the percentage of plants that match Fibonacci numbers

Then you can ask: is that percentage high enough to suggest a pattern, or could it just be random? Even a basic comparison (“This is much higher than I’d expect if it were random”) shows solid thinking.

On your board, you can show:

• Photos of your plants with labeled counts
• A bar graph showing how many plants had 3, 4, 5, 6, 8, 13 petals, etc.
• A short explanation of why plants might use Fibonacci patterns (better light, better packing of seeds)

If you want background reading on plant structures and patterns, university biology pages can be handy, like the USDA Plants Database or botany pages from sites like US Forest Service.

Project path 2: Are Fibonacci spirals really better at packing stuff?

Now imagine Leo, a 10th grader who loves geometry more than getting dirt under his nails. He’s curious about all those spirals in sunflowers and pinecones. People say Fibonacci helps them pack seeds super efficiently. But does it actually?

His question becomes:

Do Fibonacci-based spirals pack circles more efficiently than simple grid patterns or random placement?

Building the experiment on a screen or on paper

There are two main ways to do this:

On paper or cardboard

• Cut out a bunch of small circles (use a hole punch or coins to trace)
• Try to fill a larger circle using:
  • A simple grid
  • Random placement
  • A spiral where each new circle is rotated by an angle close to the “golden angle” (about 137.5°), which is related to Fibonacci
• Compare how many circles you can fit before you run out of space or start overlapping

On a computer

• Use basic coding (Python, Scratch, or even spreadsheets) to place points or circles using different rules
• For the Fibonacci-style spiral, you can place each new point at a slightly larger radius and rotate by about 137.5° each time
• Measure how much of the big circle’s area ends up filled

Even if you’re not a coding person, you can find high school–friendly coding tutorials from places like Code.org or math visualization projects from universities like MIT OpenCourseWare.

What to show on your board

• Diagrams of your different packing patterns
• A clear explanation of your rules (for example: “For the spiral, each new circle is rotated 137.5° from the last one.”)
• A table: pattern type vs. number of circles that fit vs. percentage of area filled

Then you can answer: does the Fibonacci-style spiral really do better, or is that just something people repeat without checking?

Project path 3: Fibonacci and population growth (yes, the rabbit story)

You may have heard the classic story: start with one pair of rabbits, they reproduce in a certain way, and suddenly the number of rabbit pairs each month follows the Fibonacci sequence.

Is it realistic? Not really. But it is a neat starting point for a math-and-biology style project.

Imagine Aisha, 9th grade. She likes biology but is also comfortable with spreadsheets. She decides to compare three simple models of population growth:

• Linear growth (add the same number every month)
• Exponential growth (multiply by the same factor every month)
• Fibonacci-style growth (each month’s population = sum of the last two)

Her question:

How does a Fibonacci-style population model compare to linear and exponential models over time?

How to set this up without losing your mind in numbers

A spreadsheet (Google Sheets, Excel) is your best friend here.

Create columns for:

• Month number
• Linear model population
• Exponential model population
• Fibonacci model population

Pick simple starting values, like:

• Month 1: 1
• Month 2: 1

Then fill down using formulas:

• Linear: previous month + 2 (or any constant you choose)
• Exponential: previous month × 2 (or another factor)
• Fibonacci: sum of the previous two months

After 12–24 months, make line graphs. You’ll see:

• Linear grows slowly and steadily
• Exponential explodes quickly
• Fibonacci starts slow but then starts to curve upward more sharply

Turning that into a science fair story

You can then discuss:

• Which model might fit real populations in nature (hint: nothing grows exponentially forever)
• Why the Fibonacci model is interesting but oversimplified

For background on population growth and modeling, you can look at educational pages from sites like National Park Service or university biology departments (for example, population ecology notes from .edu sites).

Project path 4: Fibonacci in art, design, and music

Not everyone wants a project with plants or spreadsheets. Maybe you’re more into drawing, photography, or music. The Fibonacci sequence sneaks in there too, mostly through the so-called “golden ratio,” which is closely related to Fibonacci numbers.

Think of Noah, 11th grade, who loves photography. He keeps hearing that famous paintings and photos use golden rectangles and spirals to look more pleasing. He’s skeptical.

His question:

Do people actually prefer images that follow Fibonacci-based layouts compared to random layouts?

Designing a simple human-subjects experiment

Noah prints or displays pairs of images:

• One image arranged using a golden rectangle or spiral (roughly based on Fibonacci ratios)
• One very similar image with a more random layout

He asks classmates or teachers to choose which image they find more pleasing or better composed, without telling them which is which.

He keeps a tally:

• How many times the Fibonacci-based layout wins
• How many times the random layout wins

After surveying, say, 30–50 people, he calculates percentages and uses a simple bar graph to show results.

He can then discuss:

• Do people actually prefer Fibonacci-based layouts?
• Or is the golden ratio hype a bit overblown?

If you do anything with human participants, it’s good practice to:

• Keep responses anonymous
• Explain briefly what you’re doing and that it’s for a school project

For background on perception and visual preference, psychology or vision science pages from universities (for example, Harvard’s Vision Sciences Lab or similar .edu labs) can be helpful.

How to make your Fibonacci project stand out to judges

You might be thinking: “But isn’t Fibonacci kind of overdone?” Fair question. The truth is, it can be, when the project stops at “Look, spirals!” and never goes further.

What makes a Fibonacci project feel fresh is how you handle it:

• Ask a real question. Not “Here is the Fibonacci sequence,” but “How often…?”, “Does it really…?”, “Which is better…?”
• Collect real data. Count actual petals. Run actual simulations. Survey actual people.
• Compare. Fibonacci vs. non-Fibonacci patterns. Spiral vs. grid. Fibonacci model vs. exponential model.
• Admit limits. Maybe your sample size is small. Maybe your model is too simple. Saying that out loud makes you sound more scientific, not less.

If you can explain your project so a curious 6th grader and a picky judge both understand it, you’re in a very good place.

Simple structure for your display board

You don’t need to overcomplicate the layout. Something like this works really well:

• Big question at the top: written as a question, not a title. For example, “Do Common Plants in My Neighborhood Follow the Fibonacci Pattern?”
• Left side – Background: short explanation of the sequence, maybe one or two diagrams, and why you chose this topic.
• Middle – Methods and Results: photos, data tables, graphs, and a short description of what you actually did.
• Right side – Conclusion and Next Steps: what you found, what surprised you, and what you would try next if you had more time.

You can also add QR codes linking to your spreadsheet, code, or extra photos if you want to look extra organized.

For general science fair planning tips and expectations, sites like Science Buddies or education pages from NASA and NOAA can give you a feel for how to frame a project.

Quick FAQ for Fibonacci science fair projects

Do I need to be “good at math” to do a Fibonacci project?
Not really. For nature-counting or art-based projects, you mostly need counting, basic graphs, and clear explanations. If you can handle simple addition and read a chart, you’re fine. More advanced math is only needed if you choose it.

Is Fibonacci more for middle school or high school?
Both. Middle school projects might focus on counting patterns in nature or simple art layouts. High school projects can dive into modeling, coding, or comparing different growth or packing strategies. The topic scales with you.

Do judges get tired of Fibonacci projects?
They do get tired of shallow ones. If you move beyond “Here are some spirals” and actually test something, compare patterns, or analyze data, you’ll stand out from the cliché versions.

Can I combine Fibonacci with another subject, like biology or art?
Absolutely. Some of the strongest projects are crossovers: plant biology and Fibonacci, population ecology and Fibonacci, or photography and Fibonacci-based composition.

Where can I learn more without drowning in formulas?
Look for educational pages from universities or science outreach sites. Many .edu pages explain Fibonacci with pictures and simple language. You can also search for “Fibonacci in nature university outreach” and stick to .edu or .org links.

In the end, the Fibonacci sequence is just a simple rule that creates surprisingly rich patterns. Your job isn’t to worship it; your job is to poke it, test it, and see where it really shows up — and where it doesn’t. Do that, and your science fair project won’t just look good. It’ll be good.