# Month: February 2015

### Fractals In Nature (By Joyce Liu)

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#exploremaths

1. What are fractals in nature?

Fractals consist of recurring shapes that creates beautiful things in nature. Fractals can be made up of simple shapes such as regular polygons, or complicated spiral patterns. Some fractals in nature include snowflakes, tree branches, honeycombs and ferns. Fractals are everywhere in nature and is usually used to describe the coastline paradox – where one coastline unable to be accurately measured due to the coastline always being too repetitive, no matter how accurate the details are of the coastline.

2. Which of the fractals we’ve looked at so far do you like best? Why?

Although we have not looked at this fractal in class so far, I like the snowflake the most as it is an incredibly small flake of condensed water, yet is still able to hold a unique and recurring shape. There are many different patterns for a snowflake – with their shapes being almost as singular as a fingerprint! Although it is possible for snowflakes to have the same design, they are still just as beautiful and unique in their size.

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### Symmetry and Fractals

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Today in our lesson, we studied the magic and beauty of fractals. We studied how to find the length of a coastline but the result was it is infinite. This is due to the length and actual size of the measuring tool you use. The smaller the length of the tool, the larger the coastline length will be.
We also studied fractals, such as the Apollonian Gasket in which a shape, drawn out of circles, could be made into a fractal which was infinite. Examples of fractals in nature include: the lightning bolt, shrubs and bushes, the veins on a leaf and sometimes trees.

My favourite fractal is the lightning bolt. This is because a lightning bolt is so bold, it seems it needs to be infinite. We look into the world around us, we are surrounded by fractals and symmetrical figures. Although we don’t always notice them at first, looking deeper into it can help explore the beauty of the object.

#exploremaths

### Tessellation and Symmetry ( By Kevin Xu)

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Tessellation and Symmetry are just another pair of things that nature and maths has given us but we are not willing to take in the intense beauty around us. Symmetry has many types such as Rotational, Translation and Reflectional. Tessellation can be found quite easily in nature if people are willing to not just look around the world they live in but look deep inside its beauty. The beehive is a classic example of tessellation as its hive consists of hexagons.The skin of a snake can be another form of tessellation along with the pineapple. Some examples of symmetry in nature are the starfruit, the human body, birds and many other examples. I learnt that nature is a form of perfection and beauty and just by the borders of any country there is perfection on the self similarity of the coastline. Nature, the real OCD ever to exist!

#exploremaths

### Music and Mathematics

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Music and Maths.Two totally different subjects with two totally different ways on passing the test. But, these two subjects actually have a lot of things in common if you pay close attention to how you make the music and how you do the maths. You may of heard people say that Music can help you with Maths. Usually, people dismiss this and get along with their live but really it can.

Throughout my lesson we viewed three videos explaining maths and its relationship to totally different things but the one that I thought really stood out was the relation between Maths and Music. I, myself, play music and this is why I paid even more attention to the video. I especially remember that a piece of string cut into certain fractions form the humble harp. I always resembled the harp as an unimportant instrument isolated by the other major instruments. Now I think the harp as a equation which equals to music. So if famous composers used maths with their music they used a data-bass!

#exploremaths

### The F

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Last lesson, I learned that mathematics is truly all around us. Our
class studied the different types of symmetry which consisted of
rotational symmetry, scale symmetry, reflectional symmetry and
translational symmetry or in other words, tessellation. Whether it’s
the beauty of a rose portraying how nature can be mathematically
described, or whether it is both the complexity and simplicity drawing
our eyes to architecture, I learned the various applications of maths.
Due to my passion of maths, I had a mindset that symmetry surrounded
us, however, the practical reasons behind how and why were unknown
before. Now my view on symmetry is much different, unique and
interesting as I have gained more knowledge of how mind-blowingly
impeccable it is. I personally highly enjoyed the previous lesson, as
I was clearly able to relate it to life itself and in addition, it
enabled me to understand the real importance of mathematics. If
anything surprised me, it was the fact that mathematics cannot only be
entirely expressed in the form of numbers, but also in the form of
nature, art, architecture and basically anything. Two examples of real
life symmetry I found where spider webs (in nature) and the Taj Mahal
(in architecture) #exploremaths

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### The Fascination behind Symmetry (by Hiya Ganju)

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Last lesson, I learned that mathematics is truly all around us. Our
class studied the different types of symmetry which consisted of
rotational symmetry, scale symmetry, reflectional symmetry and
translational symmetry or in other words, tessellation. Whether it’s
the beauty of a rose portraying how nature can be mathematically
described, or whether it is both the complexity and simplicity drawing
our eyes to architecture, I learned the various applications of maths.
Due to my passion of maths, I had a mindset that symmetry surrounded
us, however, the practical reasons behind how and why were unknown
before. Now my view on symmetry is much different, unique and
interesting as I have gained more knowledge of how mind-blowingly
impeccable it is. I personally highly enjoyed the previous lesson, as
I was clearly able to relate it to life itself and in addition, it
enabled me to understand the real importance of mathematics. If
anything surprised me, it was the fact that mathematics cannot only be
entirely expressed in the form of numbers, but also in the form of
nature, art, architecture and basically anything. Below are two
examples of symmetry I found interesting to share. One is symmetry in
nature and the other, symmetry in architecture. #exploremaths

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or confidential information or both. If you are not the intended recipient
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### Music and Mathematics (Alex Ho)

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Music and mathematics are not usually thought of to have any
sort of relationship at all. But throughout the course of the video, I have
come to realise how closely linked they are. Learning that even fractions play
a part in the notes used for playing an instrument really changed my view on it.
Before watching the video, I had only thought of the piano notes as just dots
with tails, but now I see that mathematics has a link to it, which is quite
fascinating.

In another video we learnt that although unable to hear his
music, Beethoven managed to produce beautiful musical pieces, simply through
visualising it using mathematics. To me, this really came as a shock, as I previously
hadn’t known much about Beethoven and how the composed music was appeasing to
the listener.

#exploremaths