Evolution of NumbersEvolution of Numbers

Setsuko MoriSetsuko Mori

OverviewOverview

California Mathematics Content Standards.California Mathematics Content Standards.

An essential Question & a unit question.An essential Question & a unit question.

A map of ancient civilization.A map of ancient civilization.1.1. EgyptEgypt

2.2. BabyloniaBabylonia

3.3. MayaMaya

4.4. ChinaChina

5.5. RomaRoma

ComputersComputers

Works CitedWorks Cited

California Mathematics Content California Mathematics Content Standards:Standards:

Grade SevenGrade Seven, Number Sense, Number Sense

1.0 Students know the properties of, 1.0 Students know the properties of, and compute with, rational numbers and compute with, rational numbers expressed in a variety of forms:expressed in a variety of forms:

2.0 Students use exponents, powers, 2.0 Students use exponents, powers, and roots and use exponents in and roots and use exponents in working with fractions:working with fractions:

Unit Question (2):Unit Question (2):How has a method of counting evolved How has a method of counting evolved

over time from ancient civilization to over time from ancient civilization to today?today?

Essential Question: Why are numbers important in your

life?

Imagine thousands of years Imagine thousands of years ago…ago…

what did ancient what did ancient people count? people count?

How did they count?How did they count?

Why did they count?Why did they count?

Ancient CivilizationAncient Civilization

1 23CurrentDecimal System

Five thousand years ago, Five thousand years ago, 1.1. Egyptian Civilization Egyptian Civilization: : 3000-1600 BC3000-1600 BC

Counting Geese

, ,

The ancient Egyptians built pyramids as tombs for the pharaohs and their queens.

How did they built them?

How did they calculate?

Did they take an inventory of Did they take an inventory of Pharaoh’s possessions?Pharaoh’s possessions?

Egyptian Numeration SystemEgyptian Numeration System: : 3400 BCE3400 BCE

How many symbols/numerals are there?How many symbols/numerals are there?

How many digits are there?How many digits are there?

What is the base for this system? What is the base for this system?

How does this system differ from the current decimal system? How does this system differ from the current decimal system?

What are they in decimal system?What are they in decimal system?

200200

7070

66

40004000

600600

2020

22

2.2. Babylonia, Babylonia, MesopotamiaMesopotamia: : 1750 BC1750 BC

How many How many symbols are symbols are there?there?

How do How do these these numerals numerals differ from differ from Egyptians’?Egyptians’?

Babylonian numerals on a clay tablet.

Babylonian NumeralsBabylonian Numerals

Two numerals: Ĭ = 1 < = 10

How to decipher this number?How to decipher this number?

How many place values are there? How many place values are there?

Is there a place holder? Is there a place holder?

How does base 60 work? How does base 60 work?

Sexagesimal System (base 60)Sexagesimal System (base 60)

602

601

603

600

21600 X 1 x573600 X 57 60 X 46 1 X 40 = 42,400+ + +

Sexagesimal SystemSexagesimal SystemBase 60 for TodayBase 60 for Today

1 hour = 60 minutes1 hour = 60 minutes

1 minute = 60 seconds1 minute = 60 seconds01:59:5901:59:59

02:00:0002:00:00

3.3. Mayan Civilization Mayan Civilization C.E. 300 and C.E. 900C.E. 300 and C.E. 900

The Pyramid of Kukulkan at Chichén Itzá

The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.

Mayan NumeralsMayan Numerals

What is the number in blue?What is the number in blue?

How How many many symbols symbols are are there? there?

Base 20?Base 20?

Why Base 20?Why Base 20?

Mayan Civil Calendar: 20 days x 18months + one 5 day month.

Mayan Ritual Calendar:20 days x 13 months.

Ten fingers and ten toes?

Mayans cerebrate K'atun,a ceremony that was conducted every 20 years.

4.4. Chinese Numerals Chinese Numerals

百　

千

　

万　

億

　

兆

百　

千

　

万　

億

　

兆

６　

７　

８　

９　

６　

７　

８　

９　

六

　

七

　

八

　

九

　

十

六

　

七

　

八

　

九

　

十

１　

２　

３　

４　

５

１　

２　

３　

４　

５

一　

二　

三　

四　

五

一　

二　

三　

四　

五

１０

100,000,000

10,000

100

1,000

1,000,000,000,000

一億三千六百二十九　 (equals 100,003,629)

5.5. Roman Numeration system Roman Numeration system500 B.C.E. and C.E. 100500 B.C.E. and C.E. 100

11II 11 IVIV 44

VV 55 IXIX 99

XX 1010 XLXL 4040

LL 5050 XCXC 9090

CC 100100 CDCD 400400

DD 500500 CMCM 900900

MM 10001000

CCLXXXI (equals 281) MCVIII (equals 1108)

Computer LanguageComputer Language

Two symbols: 0 and 1Two symbols: 0 and 1

Binary numeral system Binary numeral system

On or off on a circuit boardOn or off on a circuit board

0

01

10

11

100

101

00

11

22

33

44

55

110

111

1000

1001

1010

1011

66

77

88

99

1010

1111

EgyptianEgyptian 7 symbols7 symbols Base 10Base 10

BabylonianBabylonian 2 symbols2 symbols

Place valued Place valued

Place holderPlace holder

Base 60Base 60

MayanMayan 2 symbols2 symbols

ZeroZero

Place valuedPlace valued

Base 20Base 20

RomanRoman 7 symbols7 symbols Base 10Base 10

ChineseChinese 16 symbols16 symbols Base 10Base 10

Hindu-Arabic Hindu-Arabic (ours)(ours)

Decimal SystemDecimal System Base 10Base 10

ComputerComputer 2 symbols2 symbols Base 2Base 2

ReferencesReferences

http://www.ancientegypt.co.uk/menu.htmlhttp://www.ancientegypt.co.uk/menu.htmlThe British Museum (Egyptology)The British Museum (Egyptology)Http://webexhibits.org/calendars/calendar-mayan.html (Mayan Calendar)http://www-groups.dcs.st-and.ac.uk/~history/index.html(History of Mathematics Archive)http://www.historyworld.net/ (History of World)