Week 5 - The Historical Development of Number

Question 1

Numeration system

Answer 1

Numeration systems are structured methods or procedures for counting in order to determine the total units in a collection.

Question 2

Dresden Codex (book)

Answer 2

Mayan Book

The Dresden Codex contains astronomical tables of outstanding accuracy. Contained in the codex are almanacs, astronomical and astrological tables, and religious references.

Question 3

Bits and Bytes

Answer 3

Bit: Contraction of Binary Diget

• Logical state with 1 or 2 possible values: 1 or 0, yes or no, true or false punch cards, voltage, electricity, magnetism, light intensity

Byte: A group of 8 bits

• Initially a byte was the smallest numbers of bits used to encode one character of text

1 KB = 1024 bytes
USB: 16 GB
Hard drive: TB

Question 4

Roman Numeration System

Answer 4

Ancient Rome: 8th Century BC to 5th Century AD

• Roman Numerals

I = 1
V = 5
X = 10
L = 50
C= 100
D = 500
M = 1000

Question 5

Roman Numeration System

Additive examples

XX
XI
MMXXI

Answer 5

XX = 10 + 10 = 20

XI = 10 + 1 = 11

MMXXI = 1000 + 1000 + 10 + 10 + 1 = 2021

Question 6

Hindu-Arabic numeration system

Multiplicative

Answer 6

238 is not 2 + 3 + 8 = 13

But (2x100) + (3x10) + (8x1)

Question 7

Roman Numeration System

Subtraction principle

IX
XL
XC
CD
CM

Answer 7

IX = 9 (10-1)
XL = 40 (50-10)
XC = 90 (100-10)
CD = 400 (500-100)
CM = 900 (1000-100)

Question 8

Non-Standard Number Representation

Hindu-Arabic numeration system (words of numbers)

74
485

Answer 8

74 = 7 tens + 4 ones
Or
74 ones

485 = 4 hundreds + 8 tens + 5 ones
Or
4 hundreds + 85 ones
Or
48 tens and 5 ones
Or
485 ones

Question 9

Ethnomathematics

Answer 9

Describes the mathematical practices of identifiable cultural groups.

Western concept of mathematics

Appreciation of Indigenous mathematics improve out understanding of mathematics

Merging science and social justice