Tag: exploremaths

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.

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 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

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

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

#exploremaths

1. What are fractals in nature?

Fractals consist of recurring shapes that creates beautiful things in nature. Fractals can be made up of simple shapes such as regular polygons, or complicated spiral patterns. Some fractals in nature include snowflakes, tree branches, honeycombs and ferns. Fractals are everywhere in nature and is usually used to describe the coastline paradox – where one coastline unable to be accurately measured due to the coastline always being too repetitive, no matter how accurate the details are of the coastline.

2. Which of the fractals we’ve looked at so far do you like best? Why?

Although we have not looked at this fractal in class so far, I like the snowflake the most as it is an incredibly small flake of condensed water, yet is still able to hold a unique and recurring shape. There are many different patterns for a snowflake – with their shapes being almost as singular as a fingerprint! Although it is possible for snowflakes to have the same design, they are still just as beautiful and unique in their size.

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Today in our lesson, we studied the magic and beauty of fractals. We studied how to find the length of a coastline but the result was it is infinite. This is due to the length and actual size of the measuring tool you use. The smaller the length of the tool, the larger the coastline length will be. 
We also studied fractals, such as the Apollonian Gasket in which a shape, drawn out of circles, could be made into a fractal which was infinite. Examples of fractals in nature include: the lightning bolt, shrubs and bushes, the veins on a leaf and sometimes trees.

My favourite fractal is the lightning bolt. This is because a lightning bolt is so bold, it seems it needs to be infinite. We look into the world around us, we are surrounded by fractals and symmetrical figures. Although we don’t always notice them at first, looking deeper into it can help explore the beauty of the object.

#exploremaths

Tessellation and Symmetry are just another pair of things that nature and maths has given us but we are not willing to take in the intense beauty around us. Symmetry has many types such as Rotational, Translation and Reflectional. Tessellation can be found quite easily in nature if people are willing to not just look around the world they live in but look deep inside its beauty. The beehive is a classic example of tessellation as its hive consists of hexagons.The skin of a snake can be another form of tessellation along with the pineapple. Some examples of symmetry in nature are the starfruit, the human body, birds and many other examples. I learnt that nature is a form of perfection and beauty and just by the borders of any country there is perfection on the self similarity of the coastline. Nature, the real OCD ever to exist!

#exploremaths

Music and Maths.Two totally different subjects with two totally different ways on passing the test. But, these two subjects actually have a lot of things in common if you pay close attention to how you make the music and how you do the maths. You may of heard people say that Music can help you with Maths. Usually, people dismiss this and get along with their live but really it can.

Throughout my lesson we viewed three videos explaining maths and its relationship to totally different things but the one that I thought really stood out was the relation between Maths and Music. I, myself, play music and this is why I paid even more attention to the video. I especially remember that a piece of string cut into certain fractions form the humble harp. I always resembled the harp as an unimportant instrument isolated by the other major instruments. Now I think the harp as a equation which equals to music. So if famous composers used maths with their music they used a data-bass!

#exploremaths

Last lesson, I learned that mathematics is truly all around us. Our
class studied the different types of symmetry which consisted of
rotational symmetry, scale symmetry, reflectional symmetry and
translational symmetry or in other words, tessellation. Whether it’s
the beauty of a rose portraying how nature can be mathematically
described, or whether it is both the complexity and simplicity drawing
our eyes to architecture, I learned the various applications of maths.
Due to my passion of maths, I had a mindset that symmetry surrounded
us, however, the practical reasons behind how and why were unknown
before. Now my view on symmetry is much different, unique and
interesting as I have gained more knowledge of how mind-blowingly
impeccable it is. I personally highly enjoyed the previous lesson, as
I was clearly able to relate it to life itself and in addition, it
enabled me to understand the real importance of mathematics. If
anything surprised me, it was the fact that mathematics cannot only be
entirely expressed in the form of numbers, but also in the form of
nature, art, architecture and basically anything. Two examples of real
life symmetry I found where spider webs (in nature) and the Taj Mahal
(in architecture) #exploremaths

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