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1 – Numeral Systems

π. The circle has 360 ° and that fact is connected to π in a peculiar way. Look at the 360 th decimal position of π : the number 3 is in the 359 th place, the number 6 is in the 360 th place, and the number 0 is in the 361 st place. This places 360 centered in the 360 th place.

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1 – Numeral Systems

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  1. π The circle has 360° and that fact is connected to π in a peculiar way. Look at the 360th decimal position of π: the number 3 is in the 359th place, the number 6 is in the 360th place, and the number 0 is in the 361st place. This places 360 centered in the 360th place.

  2. 1 – Numeral Systems The student will learn about Numeral systems from primitive time up to modern base systems.

  3. Cultural Connection The Hunters of the Savanna The Stone Age – ca. 5,000,000 – 3000 B.C. Student led discussion.

  4. §1-1 Primitive Counting Student Discussion.

  5. §1-1 Primitive Counting One-to-one correspondences with sticks, stones, scratches or notches in bone or wood.

  6. §1-2 Number Bases Student Discussion.

  7. §1-2 Number Bases Quinary scale base 5 Decimal scale base 10 Duodecimal scale base 12 Vigesimal scale base 20 Sexagesimal scale base 60

  8. §1-3 Finger Numbers and Written Numbers Student Discussion. Numbers to 10,000 still used today. Not good for calculations.

  9. §1-4 Simple Grouping Systems Student Discussion.

  10. §1-4 Simple Grouping Systems Additive Grouping as by the Egyptian Hieroglyphics. 234 On the board! Subtraction added by the Babylonians. 234 Grouping as by the Greek Grouping as by the Greek or Roman systems. 234 234

  11. §1-5 Multiplicative Grouping Systems Student Discussion.

  12. §1-5 Multiplicative Grouping Systems A base b is selected and then symbols are chosen for 1, 2, 3, …, b – 1, b, b2, b3, … Chinese-Japanese system 234

  13. §1-6 Ciphered Number System Student Discussion.

  14. §1-6 Ciphered Number System A base b is selected and then symbols are chosen for 1, 2, 3, …, b – 1, b, 2b, …, (b – 1)b, b2, 2b2, …, (b – 1) b2, … Greek number system. 234

  15. §1-7 Positional Numeral Systems Student Discussion.

  16. §1-7 Positional Numeral Systems N = anbn + an – 1bn – 1 + . . . + a2b2 + a1b + a0 where N is then written as an an = 1 . . . a2 a1 a0. 234 in Hindu-Arabic. Babylonian using base 60. 234 Use modern notation. Using cuneiform and base 60. Mayan base 20*. Third place was 20 x 18 not 20 2 . 234

  17. ZitsBy Jerry Scott and Jim Borgman

  18. ZitsBy Jerry Scott and Jim Borgman

  19. ZitsBy Jerry Scott and Jim Borgman

  20. §1-8 Early Computing Student Discussion.

  21. §1-8 Early Computing Addition and subtraction in all systems was easy. Remember we are unfamiliar with their systems. Do you understand the addition on the top of page 23? Subtraction was similar. Physical difficulties with clay tablets, papyrus, parchment, sand trays, waxed boards, abaci, etc.

  22. §1-9 Hindu-Arabic Number System Student Discussion.

  23. §1-9 Hindu-Arabic Number System Hindus invented and Arabs transmitted about 250 B.C. Disagreement between the algorists and the abacists with the present system (algorists) winning in about 1500 A.D.

  24. §1-10 Arbitrary Bases Student Discussion.

  25. §1-10 Arbitrary Bases Base 7. Count.

  26. §1-10 Base 7 Add/Subtract Homework - Addition table with problems including subtraction. 235 seven - 156 seven 235 seven + 121 seven 235 seven + 354 seven 435 seven - 121 seven Check your work! Check your work!

  27. §1-10 Base 7 Multiply/Divide Homework - Multiplication table with problems including division. 235 seven x 121 seven 235 seven x 354 seven 121 seven 4seven 15321 seven 13seven Check your work! Check your work!

  28. Assignment Read Chapter 2 and work on your first paper.

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