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~ History of Numbers Assignment~

Year 8 Maths - History of Numbers Assignment

INTRODUCTION | TASK | ASSESSMENT | RESOURCES

INTRODUCTION
There are 3 methods of arranging numerals to form numbers:

Additive Notation e.g. Egyptian, Sumerian, Greek & Roman numeration systems
Multiplicative Notation e.g. Chinese numeration system
Positional Notation e.g. Babylonian Mayan, and Hindu-Arabic numeration systems

TASK
Your task is to research and evaluate ONE example of these numeration or number systems.
Research - your information needs to include:

History of that culture's numeration or number system
The symbols used, and the method of arranging them to form numbers; with clear examples
The use of fractions (if applicable)
An annotated record of web sites used [see Resources below]

Presentation and Evaluation - your information will be presented as a poster to the class when you will also speak on what you consider to be the advantages and disadvantages of that numeration or number system.

ASSESSMENT RUBRIC

CRITERIA	EXCELLENT	SATISFACTORY	NEEDS IMPROVEMENT
Information presented	Comprehensive range and depth of detail. Clear explanation of how that system worked and why it did or did not survive to present times.	Adequate description of the system and its origins. Some explanation of how system worked.	Not all aspects of system covered. Some descriptive facts but little explanation of how the system worked or how it has or has not survived to present times.
Examples of symbols and numbers	A range of examples provided and referred to as part of explanation.	Some examples provided.	None or very few examples provided, without being referred to in text.
Reference to fractions (if applicable)	Included as part of explanation where applicable	Included where applicable.	Not included where applicable.
Annotated record of sites used	Clear and useful annotations that evaluate a number of sites.	Sites recorded with some comments.	One or no sites recorded without any comments.
Poster presentation	High visual impact - clear and concise information, colourful, use of illustrations, appealing layout.	Satisfactory visual impact - some use of colour, illustrations included.	Little visual impact - confused or slapdash layout
Oral evaluation	Fluent delivery that indicates some thought and reflection	Some judgement made	No evidence of thought or reflection

RESOURCES
You are expected to only use these pre-selected sites. There is no need (or time) to conduct your own search.
If you wish to make electronic notes as you look at these sites, but are not sure how to do it, click here for on-line help.
Don't forget that you also need to make some comments on the usefulness of the sites you look at - so record the title, author, URL and your comments as you go. Click here to find out how to do that electronically.

Read this page first to get the topic in perspective, then click back to their home page to find useful links...
How numeration systems began http://members.tripod.com/kangwei1a14/hownum.htm
Primitive people had several ways of recording the few numbers they needed. A shepherd could collect pebbles to represent the number of sheep in a flock. Each pebble meant one... Created by students like you - but don't copy or plagiarise, do better!

The first group of sites are general ones that may be useful for more than one numeration or number system.
Click on one of these key systems to go to more specific sites:

GENERAL WEB SITES

Links to Information on Number Systems
http://forum.swarthmore.edu/alejandre/numerals.html
Excellent list of sites categorised by culture

THE DEVELOPMENT OF COUNTING SYSTEMS AND NOTATIONS
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/countsys.htm
Also follow Links to other History of Mathematics sites: http://www.scit.wlv.ac.uk/university/scit/maths/history.htm

The History of Mathematics in the Classic Cultures: Sumeria, Babylonia, Egypt, India, China, Greece, Islamic World
http://cs.beloit.edu/~chavey/M103/Classical.html

History of Mathematics Links: Mathematics in Specific Cultures, Periods or Places
Egyptian Fractions (David Eppstein, University of California, Irvine) Egyptian Unit Fractions (Kevin Brown) Ahmes, what were you thinking? (Christos Obretenov...
http://www.maths.tcd.ie/pub/HistMath/Links/Cultures.html

Earliest Uses of Symbols for Fractions and Decimals
http://members.aol.com/jeff570/fractions.html

NUMBER SYSTEMS
http://www.ndtc.org/strecnolab/bib/digital/sym/num/num_2.html

Natures Numbers
scroll down to Historical Numeration Systems
http://www.earth360.com/naturesnumbers.html

Numeration Systems and Numbers
http://www.comptons.com/encyclopedia/ARTICLES/0125/01341184_A.html

EGYPTIAN

Egyptian Numbers
http://www.mcn.net/~jimloy/numbers.html

Egyptian Fractions
http://www.mcn.net/~jimloy/fraction.html

Egyptian Multiplication
http://www.mcn.net/~jimloy/mult.html

Ancient Egyptian Numbers
http://www.noisefactory.co.uk/research/sci-math/history/hist003.html

Egyptian Mathematics Web sites
An annotated list of sites dealing with the history of Egyptian and Mesopotamian mathematics.
http://www.baldwinw.edu/~dcalvis/egypt.html

Why unit fractions?
http://www.seanet.com/~ksbrown/whyunits.htm
Uses complex language.

Mesopotamian Mathematics Page Babylonian and Egyptian Mathematics
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_and_Egyptian.html
This site is a very interesting one, as it describes the mathematical systems of both...

Egyptian Numerals
Earliest Egyptian system hieroglyphic based on the repetition of symbols for one, ten, hundred, thousand, ten thousand, hundred thousand and million. Oldest known numerals:1-2-3-4-5 6-7-8-9-10 100-1000-10000-100000-1000000...
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/en.htm

SUMERIAN

Mesopotamian Mathematics
Contains aspects of Mesopotamian mathematics including an historical timeline as well as details on old Babylonian multiplication tables.
http://it.stlawu.edu/~dmelvill/mesomath

Sumerian metrological numeration systems
By about 3000 BC, the Sumerians were drawing images of tokens on clay tablets. At this point, different types of goods were represented by different symbols, and multiple quantities represented by repetition. http://it.stlawu.edu/~dmelvill/mesomath/sumerian.html

Sumerian and Babylonian Numerals
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/sbn.htm

Mathematics & Economics.
By about 3000 BC, the Sumerians were drawing images of tokens on clay tablets. At this point,different types of goods were...
http://www.crystalinks.com/sumermath.html
Mesomath
http://www.providence.edu/dwc/mesopot.htm

GREEK/ROMAN

Greek Numerals
http://asgle.classics.unc.edu/numerals/greek_numerals.html

Hebrew and Greek Alphabetic Numeration (no history info)
http://www.cix.co.uk/~indexer/hebnum2.htm

Greek Numbers and Arithmetic
http://www.math.tamu.edu/~dallen/history/gr_count/gr_count.html

Ancient Greek Numerals
http://web.clas.ufl.edu/users/rhatch/pages/02-TeachingResources/HIS-SCI-STUDY-GUIDE/0025_ancientGreekNumerals.html

Greek Alphabet with numerical values
http://becomingone.org/hebgknum.htm

A Mathematics Lesson Plan: Roman Numerals
http://www.pwcs.edu/pwc/roman.htm

Roman Numerals Defined
http://www.mcn.net/~jimloy/roman0.html

Arithmetic with Roman Numerals
http://www.mcn.net/~jimloy/roman.html

Division with Roman Numerals
http://www.mcn.net/~jimloy/division.html

ROMAN NUMERALS History and use
http://www.deadline.demon.co.uk/roman/intro.htm

CHINESE

A Brief Description of the Chinese Number System
http://www.mandarintools.com/numbers.html
Check related links at end of article

Chinese Symbols Used For Writing Numbers
http://5dspace-time.org/Chapter6.html
Graphics to show how to write chinese numbers - takes a while to load!

Chinese Numbers
Click on a Chinese character. Animated GIF will appear here. Requires JavaScript
http://www.ocrat.com/ocrat/chargif/numbers.html

Development of Mathematics in Ancient China
"Chinese mathematics," was defined by Chinese in ancient times as the "art of calculation" (suan chu). This art was both a practical and spiritual one, and covered a wide ...
http://www.saxakali.com/color_asp/chinamh1.htm

BABYLONIAN

Why did the babylonians use a sexagesimal(base 60)numeration system
The MAD Scientist Network: Science History Subject: why did the babylonians use a sexagesimal(base 60)numeration system Date: Sun Jun 27 21:17:30 1999
http://www.madsci.org/posts/archives/oct99/939130273.Sh.r.html

Sumerian and Babylonian Numerals
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/sbn.htm
This site may help you understand why the number 60 was so often used by the Babylonians.

Mesomath
http://www.providence.edu/dwc/mesopot.htm

Mesopotamian Mathematics Page Babylonian and Egyptian Mathematics
http://www-groups.dcs.st-and.ac.uk/ ~history/ HistTopics/ Babylonian_and_Egyptian.html
This site is a very interesting one, as it describes the mathematical systems of both...

Cuneiform Numbers
http://www.noisefactory.co.uk/research/sci-math/history/hist011.html

MAYAN

Mayan Numeration
The pre-Columbian Mayans developed a fairly sophisticated system of numeration, primarily for the purpose of making calenders and keeping track of time. (A concern for quantifying the passage of time, and minding the calender, seems to have been a characteristic of many primitive peoples, and prompted much of the early record-keeping.) An example of a Mayan representation of a number is shown...
http://www.seanet.com/~ksbrown/kmath080.htm

Mayan Calender and Numerical Systems
he history and civilization of ancient peoples has always fascinated man up to date. We are going to observe Mayan Mathematical concepts ( such as numbers )...
http://www2.ucsc.edu/people/vicmuri/maya.html

The Mayan Numerical System
A number system is defined as any of various sets of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations...
http://members.tripod.com/a_sheppard/

THE MAYAN NUMBERS
The Mayan' s number system is in some respects very similar to ours. They used only 3 symbols as opposed to our 10 and at the time hundreds of symbols used in Roman Numerals.
http://www.cancunsteve.com/mayan.htm

The Mayan Numerals
The Maya of Central America used a zero hundreds of years before 876 AD, its earliest known use in India. When Europeans arrived in the Americas, they found that the abacus was in use in both Mexico and Peru.
http://www.saxakali.com/historymam2.htm

Mayan numbers
The history and civilization of ancient peoples has always intrigued modern man. Today we are visiting the Mayans and looking at their mathematics, especially their ...
http://www.vpds.wsu.edu/fair_95/gym/UM001.html

Mayan Math
http://saxakali.com/youth/mayan.htm
This is an extra wide page - scroll across the screen to see links

Math Forum: Mayan Arithmetic
http://forum.swarthmore.edu/mayan.math

HINDU-ARABIC

Evolution of Arabic (Roman) Numerals from India
http://www.gosai.com/chaitanya/saranagati/html/math/math_4.html

Graph/Hindu Arabic Numeration System
HINDU ARABIC NUMERATION SYSTEM (Base Ten Decimal Numeration System)
http://www.cleveland.k12.oh.us/parents/Math/tsld038.htm

The origin of the decimal system
http://www.answering-islam.org/Science/math.html

Islamic History in Arabia and Middle East : Arabic numerals
Modern Arabic (western); Early Arabic (western); Arabic Letters (used as numerals); Modern Arabic (eastern); Early Arabic (eastern); Early Devanagari (Indian); Later Devanagari
http://islamicity.org/Mosque/IHAME/Ref6.htm

Hindu-Arabic Numerals
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/han.htm

Hindu-Arabic Numerals in the West
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/hanw.htm

Arabic mathematics : forgotten brilliance?
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html