# Month: March 2015

### What is this pizza worth?

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First, answer the questions on this survey.

Second, check out the results here.

### Number Systems – Babylonian and Mayan [Adam Tan]

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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.

#exploremaths

### The Dozenal System (Josh Luong)

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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

People have
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.

#exploremaths

### Number Systems (By Joyce Liu)

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#exploremaths

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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### Re: Discovery or Invention? [Adam Tan]

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Discovered:

Science

History

Invented

Legal system

History

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.

#exploremaths

### Number Systems

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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.