Eddie Woo Submissions

Fractals (by Michelle So)

Today in class we learnt about how the
coast line doesn’t have a definite measurement as since the coast line is not a
straight line. Therefore, we can only get an estimate of the coastline as it
will never be definite as there isn’t a scale which can measure all of the bits
and pieces of the coastline. This is known as the coastline paradox. This
relates to fractals as there are fractal-like properties in the coastline.

 

In addition to learning about the
coastline, I also learnt a lot about fractals. Fractals are infinity complex
patterns that are self-similar across different scales. This means the fractals
goes on for infinity as it keep on repeating itself. In addition to this, I also
learnt that many fractals are found in nature. Some of these places include
coastline, flowers, river networks and many more. To me, fractals are very
striking as they are not just limited to geometric patterns but can also be
used to describe the progress in time. This is very intriguing to me as it
demonstrate how fractals are more than just shapes but instead are tools in
which are very useful to the world. 

 

Favorite
Fractal

My favourite fractal was the Sierpinski
Triangle. The Sierpinski triangle was interesting to me as it not only a very
beautiful shape, but it is also very similar to the coastline. Using the
fractal, it demonstrates how the coastline cannot me measured to an exact
number. In addition to this, this fractal was my favourite because instead of
expanding out like the other fractals, it expands inwards. Furthermore, it can
be constructed as a curve of a plane, this is known as the Sierpinski’s arrow
cave.

#exploremaths

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Eddie Woo Mathematics

A response to: the transcience of sharing

Last week, Simon Job – the creator of MathsLinks and its attendant sites – wrote a post called The transcience of sharing.

Simon is a sharer par excellence, not to mention a generally thoughtful and down-to-earth guy. So when he talks (types), I listen (read). Essentially, in his post he is posing this very valid question:

Why is sharing happening on social media (where it is transient) rather than on platforms that are clearly built for it and superior to it in almost every way (e.g. MathsLinks)?

This is a question I’ve thought about too – and it’s bugged me. Over the last few months, these have been the thoughts percolating around my head.

  1. (a) It’s where the community is active, which motivates the poster. In the right space, at the right time, it will gain a responsive audience and that response is a very powerful motivator.
    (b). It’s where people visit, every day and for no particular reason, which is how the viewer sees it in the first place. People come to dedicated sites like MathsLinks when they (i) are after something, (ii) have the presence of mind to look for what someone else has made/found first, and (iii) have the time to commit to browsing for a little while. That happens far less often than people pulling up their social media feed of choice (which seems to happen reflexively once people get to a bus stop or train station these days).
  2. Precisely because it does not aim to preserve, only the trendy and really engaging things bubble up to the top (either through Facebook’s black magic sorting algorithm or Twitter’s more organic system of retweets).
  3. I alluded to this above, but MathsLinks (and other similar repositories like TES Australia and Scootle) has become its own worst enemy by being so good. There are hundreds of objects there – which is awesome, but also means that a new user doesn’t even know what’s there or where to begin. There’s awesome stuff there but (coming back to the time issue that has already been identified) someone needs to commit to searching thoughtfully through it to find what will be useful to them in the present moment. This is an issue with faculty resource files just like it is for MathsLinks.

So what can be done to improve the situation? I have a handful of thoughts, corresponding to the points above.

  1. Clearly, MathsLinks is awesome as it is. We just need to connect it with the community more effectively. I feel like this is a market problem – it’s a great product, in a quiet spot. Stick it in the middle of George Street and it’ll go nuts because people will be exposed to it more frequently and the conversation about how good it actually is will spread from there. How practically to do that in our context is another question entirely, though.
  2. Maybe there needs to be a dedicated team (and by team, I mean more than just Simon) of people dedicated to capturing those cool posts when they come up on social media and then preserving them. We don’t want to discourage the spontaneous sharing and ensuing discussion; we want to leverage it and keep it somewhere that it can be found for future reference.
  3. Perhaps we need to do something like a “weekly featured resource”? I have considered doing something like that in my department with “my best lesson this week” as a regular feature of faculty meetings. It would just help people become aware of the riches that are hidden away there, rather than letting them gather digital dust in the cellar of the internet.

Just some food for thought.

Eddie Woo Submissions

Drawing Assignment Ideas (Alex Ho)

The weekend after receiving the AT2, I had already started.
During the lesson the notification was given and we were shown 2 other pieces
done by previous students. The first, was the eye made from shapes and the
second was a circle full of circles all overlapping like a Venn diagram. This
one really caught my eye and I had decided to use a circle as the main shape
for my task.

Using the Sierpinski Triangle and various other shapes, I
hopefully have captured a beautiful piece through various things taught in
class. Originally I was going to implement golden rectangle spirals but later
decided not to.

#exploremaths

Eddie Woo Submissions

Artwork Ideas (Terrence Wong)

For my AT2, I have not started but I have several ideas that could be implemented onto my artwork piece. One that I have is a rectangle, resembling the golden rectangle and inside filled with endless Venn diagrams, representing both set theory and fractals and in symmetry. I would have an array of colours to help visualize the picture easier and to make it look more affectionate. I think that by having 4 main points that we have covered included into a picture would not only be beautiful in a sense (hopefully) but would also show the knowledge that I have gained from being in this class.

#exploremaths

Eddie Woo Submissions

Symmetry and Tessellation (by Michelle So)

In this lesson, I learnt about the
different types of symmetry. There are 4 types, these are rotational,
reflectional, scale symmetry and translation symmetry, also known as
tessellation. Here are two of the tessellations I found interesting.

 

Tessellation – Nature

There are a lot of tessellations that can
be found in nature, the one I found very interesting was the shell of a turtle.
The shell of a turtle is interesting as it contains more than one type of
shape. Turtle shell includes irregular hexagons surrounded by pentagons. In
addition to this, it is also enclosed with quadrilaterals. The tessellations on
the turtle’s shell is very important as without the tessellations, the shell
would easily collapse, leaving the turtle defend-less as the shell is actually
part of the turtle’s body, with it being the outgrown ribs and e vertebrae of
the turtle.

 

Tessellation – Architecture.

In addition to having tessellation found in
nature, there are also a wide range of tessellation found in architecture. An
example of this is the Federation Square in Melbourne. Federation Square is
located at the intersection between Flinders Street and Swanston Street. It was
built in 26th October 2002 and has an area of 3.2 hectares. The
outline of federation square is made out of entirely scalene triangles. The
triangles are made with the dimension 1, 2, and root 5. The triangles are then  attached together in different angles creating
interesting pattern on the building façade. Furthermore, the pinwheel tiling
pattern was used in the ‘atrium’ part of the building, which is one of the
major spaces in the federation square.

#exploremaths

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Eddie Woo Submissions

Mathematics in Music and Art (By Michelle So)

Maths is everywhere around us, even if we didn’t
realise it before, it is apart of everything we learn and do. In today’s
lesson, we watched a few youtube videos about maths. During those videos, I
learnt that music is written based on intervallic relationships, which is
highly related to mathematics, this discovering amazed me as I have always
thought of music as something that couldn’t be related to mathematics. In
addition to this, I found out that Pythagoras, who is the father of
mathematics, is also the father of music! Pythagoras was the father of music as
he discovered the octave has a ratio of 2:1. It was also this formula, many
instrument were created.

 

In addition to this, I expanded my knowledge
of mathematics in nature. I found out that all nature world have a pattern of
logic, and the pattern are endless. Furthermore, I expanded my knowledge on the
golden ratio. The golden rectangle can actually be found in a pentagram, as the
two shorter lines is exactly the third line, the second and the third shorter
line is exactly the fourth line. The golden ratio also dominated the beauty of
the western world, with many of the renaissance painting using the ratio.

 

Throughout this lesson, I learnt a lot more
about mathematics and how it is surrounding all of us. Without mathematics, the
world would be completely different.

#exploremaths

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Eddie Woo Submissions

Symmetry and Tessellation in Nature (by Erik Willison)

#exploremaths
In this lesson we found that symmetry comes in 4 different kinds, these are: -rotational, 

        -reflectional, 

        -translational,

        -scale symmetry.

I found it funny that even though everyone has seen many examples of these four types of symmetry, most people could only come up with two or three types of symmetry. But despite that we aren’t very observant at times, all symmetry is beautiful as we discussed in class and we proved that by creating some of our own symmetry. We made a random shape, reflected it and then enlarged it and in doing so made both reflectional and scale symmetry. We also made a really cool spirally square thingy that is full of maths; it has scale and rotational symmetry, it has the golden spiral in an infinite amount of places plus it looks pretty cool.

And that was  basically the end of the lesson except we looked at some hexagons and had tessellation briefly mentioned to us, so here i have some examples of symmetry in nature. The most obvious example of this would have to be a beehive but I thought that saying beehive and pineapple was a cop out so I came up with a list of not common tessellating things in nature:)

-cracks in the ground on a dry day

-Any reptiles skin

-Each segment on a leaf no matter how small

-The pupil and iris of our eyes

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Eddie Woo Submissions

billiards

Billiards and Mathematics (Eric Sun)

At first glance, the game billiards doesn’t have any
resemblance to mathematics. Many would think that the diamonds around the table
are there for no reason and that it would require luck. However, throughout the
course of the video, I realise that is has little to do with luck. The lines
around the table are there for a reason and striking the ball at different
angles changes how the Q ball acts, like how striking the Q ball low so it will
spin backwards. I had always thought that it was based on luck and years of
practise But after watching the video, I now know that it has little to do with
luck and more to do with how you strike the ball and how the diamonds are there
for a reason and not there for aesthetic purposes.

#exploremaths

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Eddie Woo Submissions

Golden ration

The Golden Ratio in nature and
architecture (by Eric Sun)

Examples of
the golden ratio in architecture

1: Toronto’s CN Tower

The CN Tower in Toronto is the tallest,
freestanding structure in the world and contains the golden ratio in its
design. The ratio of the observation desk at 343 metres to the total height of
533.33 is 0.618 or phi.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2: The UN Building

The current headquarters for the United
Nations was constructed on an 18 acre piece of land in the east side on
Manhattan. The lead architect was not known for using the golden ratio in his
designs, however, a French architect on the team was known frequently to use
the golden ratio in his designs. When constructing the United Nations
headquarters, the team decided to use the ratio in a few different ways.

 

 

 

 

 

 

3: The Notre Dame

Phi and the use of the golden ratio are found in the design
of Notre Dame in Paris, France. The west façade of the church was completed
around the year 1200, and it is here where the presence of the use of the
golden ratios is visible.

 

 

 

 

 

 

 

 

 

 

Examples
of the golden ratio in nature

1:
Spiral Galaxies

Spiral
Galaxies also follow the Fibonnaci Pattern. The Milky Way has several spiral arms, each of them a
logarithmic spiral of about 12 degrees.

 

 

 

 

 

 

 

 

 

 

 

 

2: Pinecones

Similarly, the
seed pods on a pinecone are arranged in a spiral pattern. Each
cone consists of a pair of spirals, each one spiralling upwards in opposing direction

 

#exploremaths

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Eddie Woo Submissions

symmetry and tesselation

Symmetry and Tessellation (Eric Sun)

Today in class we learnt about the properties of symmetry
where we tested different methods such
as rotation, reflectional, scale symmetry and translational symmetry. Tessellation
can be found within games. A chess board consisting of 64 squares, with 2
alternating colours (usually a dark colour and
a light colour) feature a tessellation of squares, unlike a beehive, with its hexagons
and relatively same colours. 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. The completed
shape with the spirals joined, although what started off as something simple,
turned out to produce something complex.

#exploremaths

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