The History of Numbers and NumeralsDate: 12/08/98 at 22:42:09 From: Julianne Subject: History of Numbers I tried to find the History of Numbers on the Net but I still couldn't find why and how numbers have been invented, and who invented them. I could only find information on prime numbers. All I want to know about is numbers. Without numbers we can't use the phone, count cash, and so on. Date: 12/09/98 at 10:33:51 From: Doctor Rick Subject: Re: History of Numbers Hi, Julianne. This is certainly a big topic. First, we need to distinguish between NUMBERS and NUMERALS. A number is an abstract concept. A numeral is a way of writing down (or talking about) a number. We couldn't do much of anything in today's world without either of these! I don't know which of these you are interested in - maybe both! Numbers were "invented" (or discovered, depending on one's philosophical viewpoint) long before history. This happened when people realized that they could think about "how many" without needing to know "how many WHAT?" - that there is an idea of number that is separate from the world of things that can be counted. Mathematics has developed in part through the extension of the idea of number to new types of number. Mathematicians added negative numbers to the counting numbers, inventing the INTEGERS. Then they added fractions to get RATIONAL NUMBERS; then they discovered that they needed numbers that were not rational (IRRATIONAL), thereby extending numbers to the REAL NUMBERS. Later they added IMAGINARY NUMBERS to the reals, making the COMPLEX NUMBERS. There are still other things that can be called numbers, such as the TRANSFINITE NUMBERS. Many of these types of numbers were used long before they were named and carefully studied. You can search for any of these types of number on our Math Search page: http://mathforum.org/grepform.html You can also look at these sites on the history of math: http://www-history.mcs.st-and.ac.uk/history/ http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html Turning to NUMERALS, there have been many types of numerals used in various cultures. You are most familiar with Hindu-Arabic numerals (the ones we use every day), and Roman numerals. Here are some interesting sites I have found about numerals. You can find information about Roman numerals here: http://www.deadline.demon.co.uk/roman/front.htm This page shows how the Babylonians wrote numerals. http://www.phys.virginia.edu/classes/109N/lectures/babylon.html This page shows Egyptian hieroglyphics. http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/en.htm You can find an entirely different Egyptian way of writing numerals in Encyclopedia Britannica (I've got an old 1970 edition) under "Numerals and Numeral Systems." It's called the hieratic system. I haven't found it on the Web, you'll have to look it up. Here is a page about the Mayan numeral system. http://www.astro.uva.nl/michielb/maya/math.html The Greeks used letters to represent digits; see Encyclopedia Britannica again. In Hebrew the same method was used. You can find the Hebrew letters and the numbers they stood for here: http://www.amerisoftinc.com/hebletr1.htm Our symbols came from India by way of the Arabs. Here is a page that shows the early Indian numerals and the present-day Arabic numerals, along with other versions in between. http://www.islamicity.org/mosque/ihame/Ref6.htm I would like very much to find a good site on Chinese numerals or other East Asian or African numeral systems. For more information on the difference between numbers and numerals, please see: http://mathforum.org/dr.math/problems/crall11.20.98.html I hope you find the information you are looking for, whether it is about numbers or numerals. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 12/10/98 at 20:26:17 From: Julianne Subject: History of Numbers Thanks for your help earlier! But I still couldn't find the answer to my assignment. My assignment topic is 'History of Numbers.' My Outline is : * Who invented Numbers? * Where did they discover Numbers? * When did they invented Numbers? * How useful is Numbers to us? * Where did inventors get the idea to invent Numbers? I have to find the specific answers to the question above. Thanks for your time. Date: 12/11/98 at 08:28:26 From: Doctor Rick Subject: Re: History of Numbers Hi again, Julianne. I'm afraid none of these questions (except the usefulness of numbers, which is a very broad question) has a solid answer. Numbers were invented/discovered well before recorded history. I gave you pointers to the kinds of solid information we have: when particular kinds of numbers were invented, and where particular kinds of numerals were used. The latter information indicates that numbers were in use several thousand years BC in Babylon and Egypt; and the Maya, who had no contact with the old world, had numbers too. I believe numbers go back to the very beginning of the human race. The Bible says that Adam noticed that there were two of each kind of animal and only one of him; that's numbers! Look up "Numerals" in an encyclopedia, such as Britannica. You will probably find some suppositions about how numbers began in the form of pebbles or sticks, knots in a cord, etc., used to keep track of the number of animals in a herd and things like that. So counting of property was a very early use of numbers. The invention of money increased the usefulness of numbers. Then measuring of lengths for building introduced a new kind of number - not just a counting number; a length can include fractions. Now, with computers, all kinds of information are converted into numbers (binary numbers, specifically) in a computer's memory. Numbers are used by scientists to describe how the world works - expressing the laws of nature in equations. They are used by engineers, architects, musicians, ... name any profession and you can think of how they use numbers. As I said, it's a big topic! - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/