Author: Eddie Woo

Today in class we
learnt about the properties of symmetry where we tested different methods such
as rotation, reflectional, scale symmetry and translational symmetry. Before
the lesson I had only known 2 of the 4 kinds of symmetry, which were rotational
and reflectional and my knowledge for shapes was expanded. It was amazing to
see and create the scale symmetry with my own shape, which could be made
smaller or bigger depending on the scale chosen on my ruler. This only makes me
think and wonder about the unique things that shapes may have other than
symmetry and tessellation.

#exploremaths

#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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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 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 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

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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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 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

#exploremaths

Today we worked with symmetry, and how it is incorporated
from regular shapes to beautiful drawings. We know of the many types of
symmetry; Rotational, Reflectional, Scale and Translation Symmetry. Tessellation
and symmetry is all around us. Like the golden section, it is in nature, manmade
objects, everywhere. Tessellation does not only consist of a single shape
conjoined together to form a pattern, it can use more than one shape, for
example in the design of a soccer ball. These types of tessellations are called
semi-regular tessellations. We also see regular tessellations (single shapes)
in many aspects of nature, for example, the seeds in a sunflower and the hexagons
in beehives. The more we discover about maths, the more I realise that maths and nature is a perfect pair.

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#exploremaths

In class we studied some videos which described the way mathematics
is incorporated into the modern world – how math can be used in music and a game
of billiards.

It is interesting to see how music, something that we
constantly hear is mostly derived from pitch frequencies that make up geometric
series. It makes me surprised that it is possible for all the different types
of instruments and their beautiful pieces to be created from maths. Music and math
is not commonly associated with each other and to me I find it very fascinating
that they are a pair that must go together. Although this interests me, I have
very little knowledge about music (as I don’t play any instruments or sing) and
so therefore it makes me slightly confused. Even when I face a problem like
this, it doesn’t make too much difference and I am able to understand the
meaning of the videos.

In another video, we watched how the game billiards is
played using mathematical strategies. For my first impression, I was rather
confused as it appeared complicated by the heavy reliance of angles for the
strategies. I was also unsure of what was explained at first since I did not
understand how to play that game, but soon it was explained and I began to
understand. When I understood, the way the game was played made it seem like a
very hard game of techniques and mathematical strategies. I was fascinated to
see the way that the table was created – with all the markings that aid in the
strategies of a player. 

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