The Fibonacci Sequence

After watching a TED Talk by Arthur Benjamin concerning Fibonacci numbers, I was intrigued, to say the least. I have never really heard much about different number sequences and haven’t ever thought about looking into them, until now.

Benjamin talks about how there is a focus on children having to learn calculations that they will need for exams and how he would like to see maths being taught more creatively, along with being explored and enjoyed (2013). I find this very interesting. Throughout my experience with maths, the main thing that has always made me nervous is the thought of getting the answer wrong. As stated in my previous blog posts, I believe this is because I’ve always been taught what I need to know to pass and have never had a profound understanding of the subject.

The Fibonacci sequence was introduced by Leonardo of Pisa, who was also known as Fibonacci. He introduced the sequence to Western Europeans in 1202 in his book called “Liber Abaci”. The sequence begins like :

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… and so on.

It works by adding the two numbers before together, to get the next number. For example:

1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on.

The sequence is often even said to appear in nature. The Live Science website notes that an example of this is sunflower seeds. The sequence ensures that seeds are always evenly distributed. It also appears in a range of other things such as hurricanes and galaxies.

Another fascinating part of the Fibonacci number sequence is the Fibonacci spiral. The Fibonacci spiral consists of a series of quarter circles inside squares. Their dimensions being the numbers from the sequence. The squares always fit perfectly together because of the nature of the sequence.

I have found this to be very interesting as I never knew or understood what the sequence was. It has really highlighted to me that there is much more to maths than memorising formulas and calculations for exams and tests and that there is a whole world of maths out there that I don’t know about.

After watching the TED talk and looking into the number sequence myself, I do believe we should allow children more time at school to explore maths. I think this will help with their overall understanding of the subject as well as making it much more enjoyable.

References

TED (2013) The Magic of Fibonacci numbers by Arthur Benjamin. Available at: https://www.youtube.com/watch?v=SjSHVDfXHQ4 (Accessed 17 October 2018)

Live Science (2013) What is the Fibonacci Sequence? Available at:  https://www.livescience.com/37470-fibonacci-sequence.html Accessed 17 October 2018)

Maths and Art

An input i found very interesting, and thoroughly enjoyed, from the Discovering Maths module, was about how maths can be creative. I have to admit, this thought had never really crossed my mind. We spent time talking about, and looking at, tessellation’s and different forms of islamic art. Although I have seen both of these before, I never understood that maths plays such a big role in their creation.

We first discussed how many sides each shape has and took turns quizzing each other about this. We then moved onto talking about the different types of shape. This included polygons and quadrilaterals, along with talking about regular and irregular shapes. This led us onto tessellation. Tessellation is defined as “an arrangement of shapes being closely fitted together”. We were able to use what we had already discussed to talk about which shapes would be able to do this and which would not. All triangles and quadrilaterals tesselate along with a few regular shapes (squares, hexagons and equilateral triangles).

My favourite part of the input was learning about the different types Islamic art. Many examples of this kind of art have been created by tessellating different shapes.

Another example of Islamic art is the design of Islamic stars. We had the chance to create our own Islamic stars. We did this by firstly drawing a circle using a compass, then drawing a series of lines to create shapes within the circle. I found this activity very enjoyable and it highlighted to me that maths can be fun and creative. Inserted below is one I created in the workshop.

Because I enjoyed this input, I decided to try out a different form of creative maths at home. We were given the link to a digital roots website which showed how you could create patterns (similar to the image above) using digital roots. Digital roots are one digit numbers relating to a numbers times table. For example:

2 x 1 = 2 ( 2 is the digital root)

2 x 2 = 4 (4 is the digital root)

However, when the answer becomes more than a 1 digit number, you add the numbers in the answer together to get the digital root:

2 x 5 = 10 (1 + 0 = 1) 1 is the digital root

2 x 6 = 12 (1 + 2 = 3) 3 is the digital root

Following the instructions from the website, I created a circle using a compass and plotted 9 points on it, numbered 1 – 9. I then drew lines from number to number in the order of the digital roots. I did this for the 2, 5 and 8 times tables creating 3 different patterns.

I thoroughly enjoyed this activity and it has shown me that there are many different ways to learn about maths. Often in maths lessons I have felt nervous about activities and the thought of getting the answer wrong has always worried me. However, I found this type of learning to be a completely different experience. It was much more enjoyable and relaxed while still being  able to learn about maths. Therefore, I believe learning creatively about this subject is very beneficial.