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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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
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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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
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
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
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
Feedback on the videos: All of them were very interesting.
1) Donald Duck in Mathmagic land- This video was very long, almost half an hour BUT it was very interesting too.
One thing that really surprised me was how music is related to Pythagoras. It would’ve taken ages to work that out.
Another thing that surprised me was that billiards uses so much maths. The player needs to be really good with angles and needs to know the diamond system. Its incredible.
2) TedXEast- Matthew Cross- This video had a lot of interesting examples of the golden ratio and it was hard to choose only two.
The first one that surprised me was the fact that twitter and other popular websites used it. I never knew that the inventors of these websites would be so mathematical. Why would these inventors spend so much time and care about a random ratio when they need just need to make the website look attractive and useful.
The second example which surprised me was Michael Jackson’s Thriller video. It would’ve probably been a co-incidence but the fact that people go really deep into these topics is just amazing.
3) Pythagoras: How to measure beauty- I think that Human beauty is not at all about the physical appearance or numbers for that matter. I believe that it is to do with your personality and beliefs.
#exploremaths
As someone who knew a little about fractals before we started, I was interested to learn more about them.
I found it interesting that you can creat fractals such as the Mandelbrot Set by using algebra, as I had no idea it was created that way. I also didn’t realise that repeating patterns went so far into it, it is like hundreds of different fractals in one.
This fractal topic was quite interesting, and I am excited to see what our next topic is.
#exploremaths
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all three videos were amazing. I was amazed by the Golden Ratio. the lesson was entertaining….
#exploremaths
Wootube 