Month: March 2015
Babylonian Number System
As it is with most other number systems, the main purpose of the Babylonian numerals was to count. A base-60 number system proved much easier for calculations, as, previously, each number up to ten had a different symbol. The distinctive features of Babylonian numerals include:
– Only two digits are used
– The value of the digit is determined using the digit itself and the positioning of it
– Number of tens written on the left, number of units on the right
Modern usage of the Babylonian number system can be found in time: sixty seconds in a minute, sixty minutes in an hour, and 360 degrees in a circle.
One big advantage of a base-60 number system is that it is a highly composite number.
Mayan Number System
Once again, this number system is used to count. The distinctive features are:
– Base-20, as the Mayans counted using their fingers AND their toes
– Three different number symbols – zero is a shell, one is a dot and five is a line
– Sets of five (lines) are placed horizontally at the bottom and the ones (dots) are placed above it
Mayan mathematics are used today in our calendar. In Mayan numerals, numbers over nineteen were expressed with a dot representing a multiple of twenty (ie. twenty-three would be expressed with a dot over three dots). The same principal was used with the calendar, however, the upmost dot represented a multiple of eighteen. For the Mayans, there were twenty days in a month and eighteen months in a year, 360 (the five days were considered bad luck).
An advantage of using this number system is that large numbers are easier to express, and simple arithmetic is easily accomplished.
Dozenal System (base 12)
1. What is the purpose
of this number system, and what are its distinctive features?
The main purpose
for the dozenal system is to count however the main distinctive features that
this counting system has over the base 10 counting system is the number 10 we
know is written like an upside-down 2 and 11 is written as a backwards 3. The
number 12 becomes our number 10.
2. Explain where and
how this number system is used today
.The dozenal system
is rarely used today but languages such as Janji, Gbiri-Niragu, Piti were known
to have used this counting system. Units of time are seen in the dozenal system
where there are 12 months in a year, 12 signs of zodiacs and the Babylonians
had 12 hours in a day.
3. What are the
advantages and disadvantages of this number system?
considered other counting systems such as the base sixteen because it would
bring humans closer to how computers calculate. Counting in the dozenal system provides
better mental problem solving using factors of 12.
The decimal number system has a base of ten and its numbers can be either terminating or recurring where the recurring decimal can have a repeating sequence or infinitely un-repeating. Decimal notation is used in numbers that have a base ten numeral system such as the Roman numerals, Hindu-Arabic numerals, Chinese numerals, etc. The decimal system is also used in many different aspects of the modern day, for example; finding a part of an object. The advantage of this is that it is easily linked to our natural numbers – making it easy to calculate with. A disadvantage would be the inaccuracy, as mentioned before some decimals are forever recurring, which means you have to round them off.
The scientific notation system is special, as it represents
very large or very small numbers in a shorter form. Scientific notation forms
are always written as:
a x 10b
b = an integer
a = the coefficient of any real number
The number system is often used when numbers are too small
or too big to be written in their normal form with devices such as calculators
using this form. An advantage of this system is that it shortens the time to write
the actual number, which is found to be very convenient. A disadvantage would
be that the numbers can often be misread, as there may be confusion between big
and small numbers, especially if rushing.
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The concept of maths is invented, but the validity of it has always been there. Things such as the golden ratio and fractals are in nature, but humans just gave a name to it.
It’s difficult to give it a single label – discovery or invention – as both relate to each other. Formulae and theories etc. have been invented by man, but that’s only to discover what is already there. The circumference of a circle already exists, but the formula: C = 2πr has been invented to figure it out.
Currently, I don’t think I’m at the point where I can make an accurate judgment, so I’d have to conclude with – both.
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:
- What is the purpose of this number system, and what are its distinctive features?
- Explain where and how this number system is used today.
- 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!
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!