Today’s double
lesson was quite fascinating.
We learnt about
Iterated Function systems which is a method of constructing fractals.
Fractals are so cool
as it exhibits a repeating pattern.
The Mandelbrot set
was absolutely amazing.
Its so much fun
looking at pictures that repeat themselves as we look closer.
I had fun doing the
calculations and finding out whether a number is bounded or unbounded too.
#exploremaths
Ideas
Use symmetry with a polygon
(like we did with the square) and then use the 4 colour theorem on it to
make it look even more beautiful. (I am thinking of using triangles or
perhaps pentagons.)
Make up an extremely hard
bounded function and draw it.
I really want to do something
related to the Koch snowflake as it is very artistic however I was away on
the lesson and don’t know how to draw it. I also want it to have the 4
colour theorem.
#exploremaths
Hello Mr. Woo,
For this artwork project, I have the following ideas:
1. Draw a cross combined with the idea of symmetry and the 4-colour theorem.
2. make up my own fractal
3. Create my own cartoon according to the golden ratio, and I’ll colour it up using the idea of the 4-colour theorem.
#exploremaths
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For my artwork, I could either do:
1. A different take on the Golden Spiral
2. A fractal (such as the Koch Triangle) with artistic colouring
3. A fractal of my own
#exploremaths
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Video 1- Donald Duck
This video basically made us go to mathematics land with Donald Duck and explore how math is not only about numbers but it is fun. The video talked about how math is in everyday life such as nature, music and games. The math in music and how the octave had a ratio of 2:1 and that Pythagoras decided to form the harp in different ratios to produce different sounds. Also the music scale today is based of what Pythagoras formed years and years ago. Also the math used in games such as pool and that its not all about power about the tactics. I used to play pool but I never used to think pool was that tactical.
Video 2 – TED Talk
The most surprising thing about that video for me was when the person said that Pythagoras had found the beauty in the universe. I literally sat there shocked because I really didn’t believe it was possible to find the actual beauty of the whole universe. Also at that time in BC’s it was really hard to do anything with limited tools compared to now but everyone then laid the foundations for now
Video 3 – How to measure beauty
When I was watching I did believe that beauty was based of numbers, but as the video proceeded my opinion began to change to no because of the examples and how many structures include the golden ratio.
#exploremaths #eets
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there are many possiblitities for artwork on the three subjects:
1) we could use the golden ratio and create a spiral and with the spiral we can use the concept of symmetry or the things we learnt about fractals to generate either a symmetrical piece or a representation of a curved fractal.
2) we can use the pascals triangle and use it to draw the proof of the golden ratio (the squares) and have a patterned rectangle.
3) create a basic fractal and use symmetry to divide shape (trapeizium) into two and in each smaller shape we can draw the golden spiral in each divided segment which progressively gets smaller. (starting diagram is the sierpinski triangle using trapeziums)
#exploremaths.
Hello Mr. Woo,
Here are my ideas for the artwork assessment task:
1. My first idea is to have a pentagon with the diagonals joined to create a pentagram. Inside this there will be another pentagon with another pentagon inside, and so on forever. This will have the golden ratio, scale symmetry and fractals in its design.
2. The second idea is to create a Pythagorean tree with the starting triangle being a golden triangle made with the side lengths 1, 2 and root 5.
3. Third idea is to create two Levy C Curve fractals back to back to create a butterfly-like shape, possibly turned into one.
These are my three early ideas for the artwork.
#exploremaths
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This video taught me more about the principles in relation to pythagoras’ theorem and how this all fits in. As a piano player, I felt inclined in learning more of how Pythagoras was the father of music and maths and this led me to learn more about it and was highly enjoyable.
#exploremaths #eets
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So in creating a 2 dimensional project I was definitely more interested in doing fractals. In these fractals I was more interested in doing the Koch snowflake, then the sierpinski triangle and then the dragon curve. I don’t mind doing the golden ratio or a symmetry.
But my choices are
Koch Snowflake
Sierpinski Triangle
Dragon Curve
#exploremaths
1. Snowing lollipop land
My first idea is to make a tree using fractals with symmetry and spirals made with golden ratio that looks like lollipop dotted through out the land. The sun would be made of the golden ratio, hence the golden spiral and there will be snowflakes all around.
2. Gonna make a spider web out of fractals and symmetry.
#exploremaths
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