The magic of Fibonacci numbers

Math Fun for Kids: Math in Spirals

Books for Kids about Math of Spirals

It started with my son’s favorite picture book, Math Curse, where I could not get this pattern of numbers:

1, 1, 2, 3, 5 …

And who was this Fibonacci character anyway? I had a feeling that the name was not a random choice.

All of a sudden, I was reminded of my freshman year calculus class. The class went uneventfully until the second semester when we did sequences and series.

It seemed very simple at first…

A series is a series.

series is, informally speaking, the sum of the terms of a sequenceFinite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely. from Wiki Notes

And a sequence is a sequence.

sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function. from Wiki Notes


But when the test came, if I looked at the problem straight on, it looked vaguely like a series. And if I squinted a little, hmmm…. it was now looking like a sequence. I ended up with a D minus on that test. And so when number patterns come up, I get a little panicky.

Then Doodles and Jots did a beautiful post on Fractals and I started to see and understand that math exists in nature. And Imagination Soup’s post caught my eye when she posted her Spiral Investigation.

And so they inspired me. I can do this! Deep breath!

I CAN do a Mathematics of Spirals For Dummies Post. (My mathematics professor father would be so proud.)


A Fibonacci number is a SEQUENCE which is found by adding the two numbers before it together.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The 2 is found by adding the two numbers before it (1+1)
The 21 is found by adding the two numbers before it (8+13)
The next number in the sequence above would be 55 (21+34)

Can you figure out the next number? Here are a bunch of them.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169

* Is a Sequence a subset of a Series? I am still so confused! We are summing here, so doesn’t this make this series-like? Thank goodness that  this is the first time since Freshman year in college that I have to think about sequences versus series though I will probably get an anxiety nightmare tonight (the kind where you have a test tomorrow and you forgot to go to your math class all semester. yeah. hate those!)

And who was Fibonacci anyway?

The “greatest European mathematician of the middle ages”, his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa,Italy, the city with the famous Leaning Tower, about 1175 AD.

By the way, don’t confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci). from Maths Surrey


Plants illustrate the Fibonacci series in the numbers of leaves, the arrangement of leaves around the stem and in the positioning of leaves, sections and seeds. from Golden Number

The Fibonacci number sequence is evident in nature by the pattern which gets bigger and bigger from the center of the spiral as the spiral expands out.

fern spiral

I took those photos myself, but here are some more I found online.

from Sunsurfer

from Raw Inspirations

from Glass and Steel Structure

from Sulabyrinth

found this on Pinterest

Are you seeing patterns in nature now? And can you see the patterns are number patterns? Yay, we both pass! Phew!

Picture Books for Kids About Math in Nature

Math Verse by Jon Scieszka, illustrated by Lane Smith

“As close to genius as one gets in a picture book.”–USA Today* An ABBY Honor Book
* ALA Notable Book
* ALA Best Books for Young Adults
The Horn Book Fanfare
* Texas Bluebonnet Award
Publishers Weekly Best Books of 1995
School Library Journal Best Books of 1995
Booklist: Editors’ Choice Award
Swirl by Swirl by Joyce SidmanA Caldecott medalist and a Newbery Honor-winning poet celebrate the beauty and value of spirals.What makes the tiny snail shell so beautiful? Why does that shape occur in nature over and over again—in rushing rivers, in a flower bud, even inside your ear?
With simplicity and grace, Krommes and Sidman not only reveal the many spirals in nature—from fiddleheads to elephant tusks, from crashing waves to spiraling galaxies—but also celebrate the beauty and usefulness of this fascinating shape.
Blockhead: The Life of Fibonacci by Joseph D’Agnese

As a young boy in medieval Italy, Leonardo Fibonacci thought about numbers day and night. He was such a daydreamer that people called him a blockhead.

When Leonardo grew up and traveled the world, he was inspired by the numbers used in different countries. Then he realized that many things in nature, from the number of petals on a flower to the spiral of a nautilus shell, seem to follow a certain pattern. The boy who was once teased for being a blockhead had discovered what came to be known as the Fibonacci Sequence!

Growing Patterns: Fibonacci Numbers in Nature  by Sarah C. Campbell

This title deals with the biggest mathematical mystery in nature – Fibonacci numbers! Named after a famous mathematician, the number pattern is simple: 1, 1, 2, 3, 5, 8, 13…Each number in the sequence comes from adding the two numbers before it. What’s the mystery? The pattern crops up in the most unexpected places. You’ll find it in the disk of a sunflower, the skin of a pineapple, and the spiral of a nautilus shell. No one knows how nature came up with the sequence. Sarah C. and Richard P. Campbell introduce the Fibonacci sequence through a series of stunning photographs. Young readers will soon be seeing nature through new eyes, looking for Fibonacci numbers in daisies, pinecones, leaf patterns, seashells, and more.

The 14 Fibs of Gregory K. by Greg Pincus

Gregory thinks he has been born into the wrong family.  They love math and he doesn’t. Writing is his thing. When his best friend has to move away, he decides that the best way to convince his parents to send him to writing camp with her is to enter their cherished city-wide math competition. Now, he just has to figure out a math project. Fibonacci numbers come to the rescue because there is logic and poetry in their numbers! [chapter book, ages 8 and up]


Arthur Benjamin: The magic of Fibonacci numbers

Here’s a great TEDTalk on Fibocacci numbers!

Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

Thank you to Christy for her great suggestion of Vi Hart Videos Doodling in Math.

Here’s a great post on Math Myticism: Is the Hurricane Shape a Fibonacci Spiral?

To view any book more closely at Amazon, please click on image of book.

The magic of Fibonacci numbers

Follow PragmaticMom’s board Math Fun on Pinterest.

By Mia Wenjen, PragmaticMom


  1. Ann

    Thank for the link!!!

    I love tackling complicated subjects one baby step at a time. My kids really enjoyed Math Curse too – can’t wait to check out Blockhead and growing patterns – thanks!
    Ann recently posted…Mother Rabbit’s NewsletterMy Profile

    • Hi Ann,
      And thank you also for posting on same topic. It’s fun to get everyone’s take! Finally, I understand the math of spirals … it’s not so obvious!

  2. Artchoo

    I love the whole math patterns in nature thing. My mind shuts down when I have to think too much about math, but in the natural world it’s wonderful. Math Curse is definitely one of my fav. picture books as well.
    Artchoo recently posted…If Skateboards are the New Porsche, Include Your Kids in Your CrisisMy Profile

    • Hi Artchoo,
      I have to say that I never got math in nature … it was over my head so it was fun to post on spirals to finally understand the connection. Math Curse is a fun book. I am glad that other kids love it too!

  3. I just came by to tell you about Arthur Benjamin, but you found him already. I was watching his longer Mathemagic TED talk on the weekend. Do look out for it, very entertaining and inspires kids to emulate him I believe. If you have an iPad, look out for the new app, Frax, a wonderful way to play with fractals.
    Susan recently posted…Children’s Story App, My Mum’s the BestMy Profile

  4. Christy

    You should check out the Vi Hart videos Doodling in Math Class. You and your kids would probably enjoy them, and theres at least one about the Fibonacci series.
    Christy recently posted…Haiti – Thoughts about The Big Truck That Went By by Jonathan KatzMy Profile

  5. nice blog and well written for kids. will recommend to kids of my institute.

  6. Hi there. Wow! This is so fantastic. I stumbled upon your blog when I was searching “Sunflower Seed Spirals” on Google. I was looking for an image for my Facebook business page, and I saw your sunflower with the Fibonacci spiral in the center. Of course, like everyone else whose commented here, I am also so in awe of this amazing pattern found everywhere in nature. I even have a small spiral tattoo on my right ankle. 🙂 Thank you for blogging about this! It will be helpful to have books to refer my children to on this fascinating subject.

    As an aside…I recently learned Facebook does not allow business pages to use images from Google as cover photos. I am wondering where you found this image and if it is your original image, if you would mind me using it. I am a psychotherapist and wanted to have it as a cover photo because I think it’s a beautiful representation of the simultaneous journey inward, and constant expansion we all make as human beings.

    I’m really anticipating your response, so I hope you get this note! Thank you again for sharing/blogging! ~Elena Schreiber

  7. Oh, okay! Thank you so much for getting back to me. Do you mind pointing me in the direction of where you found it? Thank you for your help!

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