Month: March 2015

Fractals (David Yoo)

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Fractals are never ending, goes on forever, until the human eyes can’t see it anymore. it is one of the most beautiful type of shape that I have ever seen. Fractals can be enlarged and enlarged, part of it still resembling the original shape. Although it sounds unreal and magical, it exists all around us, like the coastline, fern leaves, rivers and tree branches. All of these are wonderful and awesome, but my favorite has got to be the Koch Fractals.

Favorite Fractal

The Koch Fractal is so simple to draw but extremely complex to our eyes. Its hexagons continue on spreading. it is extremely intriguing to our eyes, as all the fractals are. However, what makes this different to others, to me, is the fact that it resembles snowflakes. it shows the beauty of snowflakes, crafted in precise conditions in order to make such beautiful and intricate shape.

#exploremaths

The Golden Ratio in nature and architecture – David Yoo

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These are the architectures and beings of nature that have become my favorite Golden Ratios.

Golden Ratio in Architecture:

1) Parthenon

The Parthenon in Greece follow the golden ratio in different parts of its structure. The entire front face of the Parthenon closely resembles the golden rectangle. Also, the structural beam on top of the supporting poles are proportional to each other, in golden ratio.

2) Notre Dame

Notre Dame in Paris, which was built in between 1163 and 1250 appears to have golden ratio proportions in a number of its key proportions of design. Although it is inaccurate to measure by a photographic source, it is possible to notice the golden ration implanted into the structure in various places.

3)Toronto’s CN Tower

The Toronto’s CN Tower, although modern, contains the golden ratio in its design. the ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of phi.

Golden Ratio in nature

The Fibonacci Sequence or Series has a relatioship to the Golden Ratio. The Fibonacci Series shows up in the number of leaves on a plant and The Fibonaccie Wequence or Series has a relationship to the Golden Ratio.

1)The Shell

Shells are the results of a famous shape made utilizing the Golden Ratio called Golden Spirals. The Shells closely resemble this shape as seen in this picture.

Working out irregular areas

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What strategies can we use to find out the area of the top playground? What information will we need?

Fractals (Alex Ho)

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Fractals in Nature

Fractals are everywherein nature, never ending, only as far as our eyes can see. Rivers, with theirwinding channels and weird small side ones, all relatively follow the shape asthe big one, as seen in the diagram shown in class, where taking a closer lookon the small ones, show a similar shape to the main. In a video shown, therewas conclusively no way to measure the coastline, simply because having smallermeasuring equipment yield different results from larger ones. Fractals are usedto describe this coastline paradox, making it impossible to accurately measurethe actual length.

Favourite Fractal

My favourite fractal would have to be in trees. I find treesintriguing, just spending time to watch them sway to the wind as well as wonderhow each branch is capable to grow from the trunk, and have further branches.The leaves too, seeing the patterns on them, and being able to hold ontobranches and then just fall off.

#exploremaths

Fractals

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Fractals in Nature

Fractals are everywhere
in nature, never ending, only as far as our eyes can see. Rivers, with their
winding channels and weird small side ones, all relatively follow the shape as
the big one, as seen in the diagram shown in class, where taking a closer look
on the small ones, show a similar shape to the main. In a video shown, there
was conclusively no way to measure the coastline, simply because having smaller
measuring equipment yield different results from larger ones. Fractals are used
to describe this coastline paradox, making it impossible to accurately measure
the actual length.

Favourite Fractal

My favourite fractal would have to be in trees. I find trees
intriguing, just spending time to watch them sway to the wind as well as wonder
how each branch is capable to grow from the trunk, and have further branches.
The leaves too, seeing the patterns on them, and being able to hold onto
branches and then just fall off.

#exploremaths

The Essence of Fractals (Josh Luong)

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Where are Fractals in Nature?

Fractals are pretty
much just an infinite and never ending pattern where the shapes created never
end but finding one in nature may not be as hard as you think. Fractals can be
seen almost everywhere in our environment such as shorelines where they keep
splitting up into various individual rivers and the dividing branches on trees.
It’s quite intriguing how these natural occurrences can bear such a breath
taking form where it seems to be never ending.

Which Fractal is my
favourite?

Being exposed to many
fractals on Google images, it’s a tough choice to eliminate the rest and only
choose 1, however if I had to choose a fractal that I could spend my whole life
with it and it only, it would have to be the Romanesco
broccoli. It may not look like the most colourful fractal however it’s edible.
An edible fractal is all I need to make my life complete. With every mouthful
of this broccoli, its like you are consuming infinity and with that reasoning,
I don’t think any other fractal could ever be contested with the Romanesco
broccoli.

#exploremaths

Symmetry and Tessellation (Josh Luong)

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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