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Evolution of Numbers

Evolution of Numbers. Setsuko Mori. Overview. California Mathematics Content Standards. An essential Question & a unit question. A map of ancient civilization. Egypt Babylonia Maya China Roma Computers Works Cited. California Mathematics Content Standards:. Grade Seven , Number Sense

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Evolution of Numbers

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  1. Evolution of Numbers Setsuko Mori

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

  3. 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:

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

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

  6. CurrentDecimal System 4 5 3 1 2 Ancient Civilization

  7. 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 

  8. 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?

  9. What are they in decimal system?

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

  11. Babylonian Numerals Two numerals: Ĭ = 1 < = 10

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

  13. Sexagesimal System (base 60) 3 2 1 0 60 60 60 60 21600 X 1 + 3600 X 57 + 60 X 46 + 1 X 40 = 42,400 x57

  14. Sexagesimal SystemBase 60 for Today

  15. 3. Mayan CivilizationC.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.

  16. Mayan Numerals

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

  18. 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.

  19. 4. Chinese Numerals • 百　千　万　億　兆 • ６　７　８　 ９　 • 六　七　八　九　十 • １　２　３　 ４　 ５ • 一　二　三　四　五 100 1,000 10,000 100,000,000 １０ 1,000,000,000,000 一億三千六百二十九　(equals 100,003,629)

  20. 5. Roman Numeration system500 B.C.E. and C.E. 100 1 CCLXXXI (equals 281) MCVIII (equals 1108)

  21. Computer Language • Two symbols: 0 and 1 • Binary numeral system • On or off on a circuit board

  22. References • http://www.ancientegypt.co.uk/menu.htmlThe 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)

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