Math Fun for Kids: Math in 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 freshmanyear 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.

A series is, informally speaking, the sum of the terms of a sequence. Finite 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.

A 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 that 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”, 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

AND…

Plants illustrate the Fibonacci series in the number of leaves, the arrangement of leaves around the stem, and 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.

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

Patterns Everywhere by Lisa Varchol Perron

Spirals snuggle, safe and tight.

Growing when the time is right.

Center point and moving curve.

Patterns, patterns to observe.

This is a delightful way to explore patterns in nature, a foundational skill for learning and understanding math concepts! Rhyming four-line stanzas are paired with a nonfiction sidebar to further explain the pattern concepts. Colorful photographs showcase the pattern in nature. Spiral plants and animals are explored through a fern unfurling and a seashell. [nonfiction picture book, ages 5 and up]

Math Curse by Jon Scieszka, illustrated by Lane Smith