Maths meet Art – Fibonacci sequence and other amazing numbers

Recently we were studying patterns and sequences in Maths and we came across the Fibonacci sequence.  Always on the lookout for some ways to make Maths more interesting, I have spotted an opportunity to add some splash of art to our lessons. Well, Fibonacci’s numbers are not just some ordinary sequence, they are elegant and awe-inspiring. And they are not the only one. So, I invite you to join the artistic and mathematical adventure with us and explore the beauty of numbers!

Fibonacci sequence

Ok, but what is it?

The Fibonacci sequence is a series of numbers in which each number (Fibonacci number) is the sum of the two preceding ones, usually starting with 0 and 1.

Sounds too complicated? What about the story?

Once upon a time, in a magical land, there lived a remarkable golden goose. On the first day of the month, the goose did nothing. But on the second day, the golden goose laid one golden egg!

Now, here comes the enchanting part: starting from the third day, the golden goose did something extraordinary. It laid more golden eggs by adding the number of golden eggs from the previous two days.

Let’s lay it out:

1st day: 0 golden eggs

2nd day: 1 golden egg

3rd day: 1 (from the 2nd day) + 0 (from the 1st day) = 1 golden egg

4th day: 1 (from the 3rd day) + 1 (from the 2nd day) = 2 golden eggs

5th day: 2 (from the 4th day) + 1 (from the 3rd day) = 3 golden eggs

…and the golden eggs kept multiplying in this magical way!

Who wouldn’t like a goose like that?  Aah, yes I know, there was a story about the golden goose and it did not end well…

This extraordinary way of adding the previous two numbers to get the next one creates a special pattern known as the “Fibonacci sequence.” This marvellous pattern doesn’t just happen with golden eggs and golden geese – it appears in nature, too, like in the spirals of seashells and the arrangement of sunflower seeds on the flower. Math is truly magical.

Now, when we were talking about the spirals boys couldn’t understand how the numbers become spirals. Hence my idea!

Fibonacci spiral art

1. Get a big piece of squared paper, preferably with small squares (1 cm or 0.5 cm).
2. Begin in the middle and draw a 1 by 1 square.
3. Add a second 1 by 1 square next to the first one.
4. Increase the size of each new square as you increase the Fibonacci numbers in the sequence: 2 by 2, 3 by 3, 5 by 5, 8 by 8, and so on.
5. Now, create a spiral by starting to draw it in the first square and continuing it into the next squares.

This way, you’ll be creating a beautiful Fibonacci spiral art piece on your squared paper. At the end colour the squares with different colours and add some patterns, to make it even prettier.

Fibonacci sequence is not only a fascinating mathematical concept, but it also appears in various aspects of nature, art, and architecture, contributing to its widespread fascination. The ratio of consecutive Fibonacci numbers converges to the golden ratio, a mathematical constant that often appears in design.

Fractals

Now let’s dive further into the enchanting world of mathematics where numbers and patterns come alive! Have you heard about fractals? These are complex yet amazing geometric shapes that are created through repeating patterns.

They are like magical drawing that keeps repeating itself, no matter how much you zoom in. It’s like having a magical shape that appears in different sizes, and when you look closer, you see the same shape over and over again, like a never-ending pattern adventure.

Think of a tree: the branches look like smaller versions of the whole tree, right? Well, a fractal is a bit like that but with crazy, wiggly shapes that repeat themselves.

A fractal is like a magical pattern that loves to repeat itself and create beautiful, detailed shapes, making art and math a really cool team!

Fractal Fun: Drawing Sierpinski Triangle

Start with a Triangle: begin by drawing a large equilateral triangle in the centre of the paper (preferably squared or graph paper for accuracy). This will be the base of your fractal. You can use a ruler to make sure the sides are equal.

Inside the large triangle, draw three smaller triangles by connecting the midpoints of the sides of the large triangle. You should now have four triangles.

Choose one of the smaller triangles you just created. Repeat the process for this smaller triangle: divide it into three by connecting the midpoints of its sides.

Keep going! Select one of the even smaller triangles you just drew and divide it into three again. You can continue this process as many times as you want.

Fractals can be found in nature, like in snowflakes or leaves.

Once you’ve drawn your fractal, you can get creative! Use coloured markers or pencils to fill in the triangles with vibrant colours or patterns. This will make your fractal even more visually interesting.

Tessellations

Tessellations are patterns made by repeating shapes without any gaps or overlaps. It is the perfect activity to add to lessons about symmetry and geometry. M.C. Escher’s tessellations are famous examples.

This hands-on tessellation activity not only reinforces geometric concepts but also allows children to express their creativity through art.

Choose a shape to work with. Start with something simple like a square or hexagon. Using plain paper or cardstock, have the children create a template for their chosen shape. For example, if they choose a square, they should draw a square on the paper.

Repeat your chosen shapes across the paper, making sure that the shapes fit together without any gaps or overlaps. You can rotate, flip, or slide the shape to create the tessellation. Encourage the children to decorate their tessellation using markers or coloured pencils. They can use different colours or patterns to make their tessellation visually appealing.

When you get used to the idea choose more complex shapes for your tessellations.

Other ideas to add a splash of art into maths

There are several interesting sequences and patterns that children can draw to explore the fascinating world of math and art. Look at these suggestions:

Pascal’s Triangle

Draw Pascal’s Triangle is a mathematical triangle where each number is the sum of the two numbers directly above it. Children can colour in the triangle based on even and odd numbers or create interesting patterns.

100 number charts

Creating a square chart of numbers from 1-100 and then colouring different patterns (every even number, every 5^th, each column with different colours etc.)  makes a great hands-on activity to help children visualise numbers. This later will tremendously help with addition and subtraction.

Symmetry

Explore symmetrical patterns by drawing designs that are identical on both sides. This can involve drawing shapes, letters, or even animals with symmetrical features. Encourage children to experiment with colours and decorations to make their pictures visually engaging.

I hope you enjoy the artistic and mathematical adventures! They not only enhance the love of mathematics but also promote creativity. Win, win!