# Month: August 2014

### Artwork ideas (by @divyav99)

Three artwork ideas that I am interested in creating include;

1. The Sierpinski’s carpet with the Golden Ratio Spiral embedded within.

2. Sierpinski’s Hexagon/ Pentagon

3. Apollonian Gasket

#exploremaths

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### Video Lesson- Catch Up (by @fufujackattack)

Hello! this is a catch up on the 3 video lesson!

1. Donald duck in Mathmagic land

This video was a great fun to watch as it present mathematical ideas including

How numbers can be easily found in nature (physical world)

The world is made up of simple shapes

Pythagoras’ theories

The pentagram and golden rectangle and their amazing stories

Maths needed for the creation of equipments

Thinking mathematically

The two ideas that I found interesting were the pentagram and maths was a vital part of music. Apart from the fact that the golden ratio can be found in a pentagram (Golden ratio is in everything I swear 🙂 ), I found out that the pentagram is also a symbol for many other things. For example, the points of a pentagram can represent the elements fire, water, wind, earth and spirit. Another idea I researched further into was how maths help design and produce music. Maths has helped fine tuned the notes of the instruments and also provide a sense of rhythm for music.

2. TED talk

The TED talk provide an interesting overview of how maths is beautiful. The 2 things that I found surprising and unusual are the fact that the golden ratio is actual everywhere. I knew it was everywhere but I truly did not know it was LITERALLY everywhere! From the video he talked about how the golden ratio can be found our body parts and even on the painting of Mona Lisa.

3. How to measure the beauty of mathematics

“Is human beauty just about numbers?”

I think not. Now many can argue that physical beauty can be related to maths and it may enhance the physical feature. However, I believe that human beauty is more that what meets the eye. Human beauty is made up of both physical features and also their personality, I think that personality may be one of the only things that cannot be interpreted through numbers. Therefore, I don’t believe human beauty is just about numbers.

Yay!

#exploremaths

### Fractals & Iterated Functions (by @divyav99)

The fractals lessons, especially when we designed the fractals in groups was rather enjoyable. Starting off with a single equilateral triangle and bisecting it over and over again to achieve not only countless triangles but also intriguing patterns was quite amazing.

When we started learning about Iterated Functions it was hard to believe that complex mathematical equations as such lead to form such beautiful fractals as illustrated in the graph at the end, the ‘Mandelbrot Set’. Exploring into bounded and unbounded sequences and how they relate to one another was confusing but also pretty cool. As well as this, learning about imaginary numbers and real numbers was interesting as I would have not thought that imaginary numbers could be used in such ways to produce equations and in the end an astonishing graph.

#exploremaths

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### AT2 ideas (by @fufujackattack)

Hi Mr Woo,

These are the 3 ideas for AT2!

1. SIERPINSKI’S TRIANGLE PORTRAYED IN 3 DIFFERENT WAYS

Have a huge equilateral triangle and divide it in to 3 sections. The top section can be the Sierpinski’s triangle through the trapeziums drawings. the middle can be the original Sierpinski;s triangle. The last section would be the pascels triangle portraying the sierpinskis triangle.

2. PYTHAGOREAN TREE BONSAI

Create a Pythagoras tree and draw a bonsai pot around it. Maybe even include a snail/hermit crab with the golden spiral shell!

3.STAR FRACTAL SNOWING

Have a snowing scene with the snowflakes as star fractals!

4. Possibility of a combination of 1, 2 and 3

Yay!

#exploremaths

### Fractals

Hello!

In the fractals lessons, we learned about how fractals are shapes that have the same recurring pattern at every magnification. I was really surprised to learn that fractals can be found all around the world physically and through numbers too. The construction of our very own fractal was great and it gave me the starting insight to how fun fractals can be!

We also explored fractals through iterated functions too. The bounded and unbounded sequences amazed me as I would never have thought about fractals in numbers. The Mandelbrot set was the best part of the topic on fractals as it gave me a visual representation of fractals through the complex plane.

Yay!

#exploremaths

### Golden Ratio (by @natashaaaaaa_xo)

Hey sir,

I found the golden ratio very fascinating. I was shocked to find out

that it appears in so many places, especially old architecture. I

found it amazing how some of the 20th century architects had

proportioned their work so precisely, and in the form of Golden Ratio.

#exploremaths

### Change my ideas for artwork (@kewalbro)

I was willing to do the sierpinski triangle somewhere in my artwork. So what I decided to do is that I draw a human body part and place fractals in them. So if you think any of my ideas are good, which one do you think I should.

Draw a eye and place a spiral rose inside it. On top of this have the 4 colour theorem inside it

Draw the dragon curve and place the 4 colour theorem in it

Draw the Koch snowflake, where each triangle contains the Sierpinski Triangle

#exploremaths

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