Evolution of Numbers Setsuko Mori Overview California Mathematics

Evolution of Numbers Setsuko Mori

Overview California Mathematics Content Standards. An essential Question & a unit question. A map of ancient civilization. 1. 2. 3. 4. 5. Egypt Babylonia Maya China Roma Computers Works Cited

California Mathematics Content Standards: Grade Seven, Number Sense 1. 0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms: 2. 0 Students use exponents, powers, and roots and use exponents in working with fractions:

Essential Question: Question (2): in your Why are Unit numbers important How has a method of counting evolved life? over time from ancient civilization to today?

Imagine thousands of years ago… what did ancient people count? How did they count? Why did they count?

System Ancient Civilization

Five thousand years ago, 1. Egyptian Civilization: 3000 -1600 BC , 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 Pharaoh’s possessions? Counting Geese

Egyptian Numeration System: 3400 BCE How many symbols/numerals are there? How many digits are there? What is the base for this system? How does this system differ from the current decimal system?

What are they in decimal system? 4000 200 600 70 20 6 2

2. Babylonia, Mesopotamia: 1750 BC How many symbols are there? Babylonian numerals on a clay tablet. How do these numerals differ from Egyptians’?

Babylonian Numerals Two numerals: Ĭ = 1 < = 10

How to decipher this number? How many place values are there? Is there a place holder? How does base 60 work?

Sexagesimal System (base 60) 60 3 60 2 1 60 0 60 21600 X 1 + 3600 x 57 X 57 + 60 X 46 + 1 X 40 = 42, 400

Sexagesimal System Base 60 for Today 1 hour = 60 minutes 1 minute = 60 seconds 01: 59 02: 00

3. Mayan Civilization C. 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 Numerals

What is the number in blue? How many symbols are there? Base 20?

Why Base 20? Mayan Civil Calendar: 20 days x 18 months + 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.

5. Roman Numeration system 500 B. C. E. and C. E. 100 I V 1 5 IV 1 IX 4 9 X 10 XL 40 L 50 XC 90 C 100 CD 400 D 500 CM 900 M 1000 CCLXXXI (equals 281) MCVIII (equals 1108)

Computer Language Two symbols: 0 and 1 Binary numeral system On or off on a circuit board 0 01 10 11 100 101 0 1 2 3 4 5 110 111 1000 1001 1010 1011 6 7 8 9 10 11

Egyptian 7 symbols Base 10 Babylonian 2 symbols Place valued Place holder 2 symbols Zero Place valued Base 60 Roman 7 symbols Base 10 Chinese 16 symbols Base 10 Hindu-Arabic (ours) Computer Decimal System Base 10 2 symbols Base 2 Mayan Base 20

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