Number Systems

We have spent so many years doing maths with the same set of numbers that we often forget that our way of writing numbers is just one way among many. We use the Arabic numerals in Base 10, but there are many alternatives each with their own story. For two other number systems, research the following:

  1. What is the purpose of this number system, and what are its distinctive features?
  2. Explain where and how this number system is used today.
  3. What are the advantages and disadvantages of this number system?

Put these into your own post and submit them by the end of the lesson!

Is Mathematics invented or discovered? (By Kevin Xu)

The question remains as if mathematics is discovered or invented. This question is a good one as there are sides to both but the one side I think is the answer would probably be invented. For starters, the word ,’mathematics’, is invented because you can’t discover a word. You can only invent them. But the main point why I think think that mathematics is invented is because I think that maths is just another language such as French, English, German etc. You can’t say that you discovered something that has to follow this certain rule and say it’s true just because it’s true if you follow this rule. Maths is basically just a language in which you can present your understanding much easier. For example, in the English language, the word ball represents the round object. In maths, we can say that two represents two object in a set. Sentences are the same thing. In English, “Can you pass me the ball so I can bounce it on the wall?”, is easier than saying “Can you walk over here and hand me the round object so I can project it off a stable piece of structure and make it project back to me?”. See what I mean? It would kill the younger adults of this world because they would be too lazy to say a massive long sentence when they could simply say it in a shorter way. Maths is the same. A sentence in maths could be 2+2=4 instead of saying two sets of an object put together with another two sets of an object would combine to be 4 sets of an object. So I would stick to this opinion and say that maths is invented and is getting developed everyday to make our life simple but only just a bit is discovered on basically how you would interpret the word ‘mathematics’. But, I’m not going to do that because I spent enough time trying to translate sentences into a harder way of saying it so have fun with the word mathematics!

#exploremaths

Was Mathematics Discovered or Invented? (Alex Ho)

Mathematics is a concept that leans more towards being an
invention than a discovery. Mathematics is an invention based on a discovery. Humans
were the ones who invented the names and characteristics of math. Giving
equations and numerals names, like the basic 1, 2, 3, etc and 1 + 1. We give what
we have already seen in nature, a way for us as a whole to easily understand and
know what is going on, like a language. Golden ratios our everywhere within
nature, this was already there long before we discovered it but we invented the
name “golden ratio” for it. 

#exploremaths

Mathematics, a discovery or an invention? (by Hiya Ganju)

Is mathematics an invention or
discovery? I believe that mathematics is in reality, an invention based
discovery, meaning it is more of an invention. Mathematics is a tool used by
humans to record, describe and explain discoveries about nature. Mathematicians
have the resources and materials which have been discovered, but they invent the
theories and formulas themselves. You can’t look around, search or discover
maths because all the elements that make it up and everything that involves it,
already exists. Maths is a language which has been invented. The truth is that
we need to create and invent our own ways to prove why something is true
mathematically. In order to understand the environment, its artistic instincts
and to engage in absorbing intellectual activity from the human perspective,
the concepts, axioms and theorems established, have been created by
mathematicians. From Pythagoras’ Theorem, to Newton’s Universal Law of
Gravitation, to Einstein’s Theory of Relativity, we can conclude that humans
have created the most intelligent and beautiful concepts in mathematics. Maths
cannot be found, searched for or discovered, it requires to be resolved using
an invented method in the form of a theorem, formula or simply a process.

#exploremaths

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Is the maths an Invention or Discovery? (Josh Luong)

Maths has been implemented into
everyday life and is used all the time however was it invented by humans or is
it natural and we happen to stumble across the phenomenon. I believe that
mathematics was invented and created by humans in a way where people can
understand the concept easier that was already here. Like language used to
describe an object where that object was already in our world but we need a way
to explain so humans created languages. In a similar way, mathematics was in
our world however there had to be a way to explain the concept and so we used
numbers, formulas and notation. As simple mathematics evolved from addition and
subtraction into more advanced maths we keep on inventing new way to describe
the discovery with our formulas and equation.   

#exploremaths

Is Mathematics Discovered or Invented? (Terrence Wong)

Is mathematics discovered or invented? The answer is primarily based on what you define ‘mathematics’ is. In one, maths can be described as being discovered, as numbers were always around. Form our recent studies in class of the golden ratio and golden spiral, it is evident that these have always been around in nature, we just needed to find them, not invent them. Hence one side of saying maths can be discovered. 
But on the other hand, maths can also be invented. Based on a simple analogy of creating something from something already discovered. Are you really discovering something? Or inventing something new. From the computer analogy given in class by none other than Joshua Luong, a computer is made from raw materials already discovered. So did you discover the computer or actually invented the computer? We can take this into terms of maths. The formula for Pythagoras’ Theorem. We had built up to that from numbers, which were discovered, but the formula was invented as it was not previously noticed or made. 

So in conclusion, the discovery and invention of mathematics can vary, depending on how you interpret ‘mathematics’ as a whole. I personally think that maths, and all of its components, is invented. 

#exploremaths

Discovered or Invented?

#exploremaths

Maths, although not certain, is most likely under the
category of discovery, as numbers were always there. There are a “number” of
things in the world, therefore this comes naturally. Despite this, it could be
invented as the Aboriginal people used only one, or many and had no number
system. In my opinion, I believe that maths was discovered and then inventions
were developed from the discoveries. Maths is its own language, as the natural
numbers are in nature and ever since then, humans have been inventing their own
formulas and mathematical theories. Therefore, maths was firstly discovered.

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MATHEMATICS IN MUSIC AND ART

Maths
rotates you, nature, our solar system, and the sun. Maths is present in
everything the computer your reading this submission your keyboard even the red
pen you use to mark papers. It all rotates around you but is it hard to believe
that the sound waves you hear when listening to the latest Ariana Grande song
is maths.

In
today’s lesson we watched a TED video explaining the intervallic relationships
in music is all maths. Amazing me I wondered how this was discovered and proof
towards this as it was hard to believe. The video explained that the western
scale you play on the piano is actually made by the same person who created the
Pythagoras Theorem. The father of mathematics was also none to be the father of
music. In the video it explained how Pythagoras discovered the octave has a 2:1
ratio. It was this formula that many instruments grew out of including the
guitar and piano.

This
lesson brought full amazement to me having my mind to seek through many
different aspects of our world were maths is applicable. God’s beautiful
creation has resulted in maths.

#exploremaths

  

SYMMETRY AND TESSELLATION

In
class we have discovered interesting properties of symmetry and tessellation as
we applied four different kinds of symmetry such as rotation, reflectional,
scale and translational symmetry. In past the title, ‘symmetry and
tessellation’ had been a very vague title having to think that such thing has
no use in maths.

That
specific lesson presented the knowledge I need to seek symmetry and
tessellation from a very different perspective in result of learning scale
symmetry with a random shape consisting 5 sides, of my choice that was made
smaller or bigger depending on the scale you chose. We also created very
interesting spiral like thing. It presented very in depth mathematics involving
a scale and rotational symmetry as well as the golden spiral in infinite
amounts.

 In conclusion after observing what amazing
things you can present using symmetry and tessellation, my mind ponders through
the vast topic of symmetry and tessellation and how it plays its own role in
mathematics.  

#exploremaths