A brief history of maths
This is my first education related post,since the time I have entered the education sector. The mathematical world would be 3 part post, where I will be talking and posting about the development and evolution of maths and in the last part of this series will talk about the math around us!!
History of numbers and the number system
The concept of numbers probably originated with the need to count how many things are there in a collection of things. Thus, methods like fingers, pebbles in containers, marks on clay tablets (present day tally marks), notches on sticks, and knots on cords were developed for keeping records and counting of numbers.The knots,notches,marks either represented a single number or a group of numbers.
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| Ishango Bone & associated history |
As the civilizations grew and bureaucracy rose, the system of trades & taxes evolved, size of numbers increased, which lead to the development of more and more complex numbers and number system.
More recently, during the past 2,000 years or so !!, various systems of writing have been used to represent numbers. The decimal system or the base 10 system which is also known as Hindu-Arabic number system was actually discovered in India
504=5x10^2+0x10^1+4x10^1
The Roman number system, which is still used for some purposes (but rarely for calculation), is made up of a few letters of the alphabet and rules for combining them (for example, IV for four, X for ten, and XIV for fourteen. The roman system didn’t have any symbol for zero,besides that it was based on addition of numerals- which was a major drawback of this system hence didn’t find much application except in watch dials!
eg: if i had to write 34 i will be writing XXXIV.=10+10+10+4 and I had to write a million it would take me about half a million digits to represent it!
There is one more system around which our whole world revolves. It is the binary system—the mathematical language of computers and almost all the electronic gadgets which we use. Binary language uses just two symbols, 0 and 1, which can be combined in exponential form to represent any number. Eg:
5=101=1x2^2+0x2^0+1x2^0
6=110=1x2^2+1x2^1+0x2^0
Notice the decreasing power of 2 which is same as we observe in decimal system.
Similar to binary system there many other number systems like hexadecimal (base 16) & octadecimal( base 8) which are used to represent bits and bytes in the world of computers.
Watch this interesting video which covers how the maths has evolved in the the ancient time.
Understanding Numbers:
Whole numbers:
There are different kinds of numbers. The numbers that come from counting things are whole numbers, which are the numbers we mostly use in everyday life. A whole number by itself is an abstraction for how many things there are in a set but not for the things themselves.
If I say 1 million, it may mean 1million Rs/dollar/pounds, cars, population of city, virus population in a sample etc etc!. In most practical situations, we want to know what the objects are, as well as how many there are. Thus, the answer to most calculations is a magnitude and a label connected to it in other words a number connected to a label.
Let us take an example:
If you traveled 160 Km in 4 hours, your average speed was 40 Km per hour, not 40. In this instance, 160, 4, and 40 are numbers/magnitudes; Km, hours, and Km per hour are labels. It is the labels which give meaning to numbers.
Without the labels numbers don’t have any real significant application. This reminds me of my school days where a ½ mark or 1 mark was deducted whenever the units were missing from the final answer!
Similarly when we teach kids counting on fingers it is important to realize that it is the number of fingers we are counting and not just reciting numbers.
thought source:
http://www.scribd.com/doc/58790528/All-About-Science
http://www.project2061.org
http://darkwing.uoregon.edu/~moursund/Math/mathematics.htm
Labels: education, history of mathematics, math, number
posted by Vaib's @ June 27, 2011
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