Flashcards
Test 1 Review
Cards in this deck (70)
- 1What 3 examples do we have for tallying and briefly explain them?- The Ishango bone: Earliest form of a tally stick (Possible Lunar/Birth Calendar)
-The British Exchequer tallies: tally sticks, used for debt of citizens (split into two, one for cutter and other for citizen)
-The Quipu: a form of strings, knotted together to form rows (base of 10), used for events related to the Incas' calendar - 2What is tallying?Primary function is to record serially an ongoing enumeration, which is different from representing a final count.
- 3What is the Ishango bone?-One of the earliest known examples of a tally stick
-Possibly a lunar calendar or a birth tracker - 4What is the precursor to written numeration?Tallying
- 5What are double tallies?-They're used for keeping record of deliveries, labour, commercial and financial transactions
-Way to keep track of transactions between two parties - 6What is an example of double tallies and explain what is is.-The British Exchequer:
Sticks with marks on them to display debt owed
Broken into two, one for the "cutter" and the other for the debter.
A way to keep track of debt - 7What is a quipu, who was it made by, and what was its purpose?A form of tallying using multiple string and knots in layers.
-Made by the Incas
-Early writing instrument for administrative purposes - 8What were the two things the Spanish did while conquering the Incas?-Translated all the quipus into written data.
-Once mostly translated saw the quipus as idolatrous towards the incas, so claimed them to be the devil and destroyed all they could. - 9What does abakion mean, for which object is it used for and what did the Romans convert/translate this to?-"table without legs"
-Was the title of the Counting Board
-Converted to Abacus - 10What is a counting board?-Was a very common mean of calculation
-A flat surface marked with lines, on which pebbles or counters were placed and moved to perform arithmetic operations - 11What calculation process was used before the counting boards?The counting of fingers
- 12What year were the British Executive Tallies from?1200s
- 13What source do we have of counting boards?-The Darius Vase of the fourth-century
-Depicts a royal treasurer counting coins on top of a table - 14Who used hand-held abacus'?The Romans
- 15What gives us the term "bank"? And who would be using it?The use of counting boards on tables in early-modern Italy
Merchants, money lenders, and money exchangers. - 16What were the counting boards called for China, Japan?China - Suan pan
Japan - Soroban
Important:
Each type uses a different calculation technique - 17What did the Europeans replace the counting board with? What art piece exemplifies this?-The pen-and-paper technique
-The cover of the Margarita Philosophica by Gregor Reisch - 18What type of numerals used pen-and-paper?The Hindu-Arabic Numerals
- 19What were the textbooks called that explained the Hindu-Arabic numerals?Algorisms
(or known today as, algorithms) - 20What does the Margarita Philosophica display?-The competition between both algorithms of the Hindu-Arabic numerals and the counting board.
-The female personifying the overseer of algorithms. - 21Who wrote the Margarita Philosophica?Gregor Reisch
- 22What two non-Hindu-Arabic numeral systems represented the final values of the counting board?-Greek
-Roman - 23Name the 6 step process from tokens to written numerals.-Simple tokens
-Complex tokens
-Clay envelopes
-Token imprints
-Tablets
-Written Numerals - 24What is the difference between simple and complex tokens?The simple tokens were just shapes that only described general labour and the complex were shapes with engravings on them that represented what exact type of inventory it was
- 25What was special about clay envelopes?Inside were multiple tokens to show what stock the village had
- 26What was special about tablets?-Shapes on a piece of clay to represent stock type and amount
- 27What were envelopes, token imprints and tablets made out of?Clay
- 28What step comes after tokens for the race of written numeration?-Tokens to token imprints
- 29What are token imprints?Imprinted tokens on clay to represent stock in lesser space
- 30What is the difference from token imprints to tables?-Token imprints literally were just imprinted by tokens
-Tablets are manually drawn figures - 31Written numeration came from what form of stock tracking?Clay tablets
- 32Why did concrete counting form abstract numbers?The simplicity of mathematics was trying to be understood from keeping track of stock to understanding the multitudes of numbers
- 33What 5 systems of main cultured numerals have we focused on?-Ancient Egyptian
-Roman Numerals
-Babylonian Numerals
-Mayan Numerals
-Hindu-Arabic numerals - 34What 2 numeral systems were there for the Ancient Egyptians and explain what they are.-Hieroglyphic Numerals
-Decimal (Base 10)
-Cumulative
-Additive (Not positional)
-Hieratic Numerals
-Decimal
-Ciphered
-Additive - 35What example do we have of Hieroglyphic Numerals and what does it display?The Narmer macehead
-Displays summary of stock of cows, goats and captives - 36What are Roman numerals?-A decimal system with a sub-base of 5
-Cumulative, but modified by subtraction rule
-Additive - 37What's the subtraction rule for the Roman Numeral system?Any small value in front of a bigger value is subtracted.
- 38What value is XCV?95
- 39What numeral system is this?Babylonian numerals
- 40What numeral system is this?Roman Numerals
- 41What numeral system is this?Hieratic numeral
- 42What is this?The Ishango bone
- 43What numeral system is this?Hieroglyphic Numerals
- 44What were Babylonian numerals?-Sexagesimal (base sixty) with sub-base ten
-Cumulative within powers of the base positional
-Used for positive integers and fraction - 45What were Mayan numerals?-Vigesimal (base 20), except for the third place-value
-Cumulative with sub-base 5
-Positional (maybe), with empty-position sign - 46What is the positional principal?A system of numerals where the digits/symbols acquire their value based on their position.
-Also based on the value of the base - 47What examples do we have of the positional principle?-Counting boards
-Hindu-Arabic numerals
-Possibly Mayan numerals - 48Are Mayan numerals positional or additive?Most Mayan numerals were used for recording of dates. So possibly Calendrical but hard to define based on either.
- 49What were hindu numerals?-Decimal
-Ciphered
-Positional
-With empty-position sign (the value of '0') - 50What 2 people brought Hindu numerals west and what were their positions?-Severus Sebokht (Syrian scholar) wrote in 662
-Muhammad Ibn Musa al-Khwarizmi wrote book called "Book on the Indian Calculation" in 825 - 51What was the opinion of the Islamic Empire towards the Hindu Numerals?-Avoid using them because it requires materials to use. They'd rather use finger-counting.
- 52What years did the Hindu system appear in Europe and how?-1000-1100 appear in Spain and Italy
-Latin versions of al-Kwarizmi's algorisms appear with "Dixit Algorismi" in Latin
-1202, Leonardo of Pisa, Fibonacci, writes "Liber abaci" (The Book of Calculation), addressed to busineesmen - 53What is the importance of Fibonacci's Liber Abaci?Talked about the Hindu Numeral system and defined the 9 digits (1-9)
- 54What is also the name of Fibonacci?Leonardo of Pisa
- 55What other issues were there with the Hindu-Arabic system?-Signs have no fixed value and numbers appear to be written backward
-Digits not yet standardized, can be falsified too easily - 56What is the problem with the zero sign?In Greek theoretical mathematics a number representing nothing would be self-contradictory for it to be no number at all.
It was also counter intuitive that a sign of no value could multiply value signs to its left. - 57What kind of sign is zero?A meta-sign, because it is not a symbol of any object, concrete or abstract.
- 58What year did the Hindu numeral system emerge?600s
- 59What city banned Hindu-Arabic numerals figures from book keeping?The city of Florence, Italy, in 1300
- 60What historical sources do we have of Ancient Egypt mathematics?2000 - 1000 BCE the Papyri were created.
The Rhind and the Moscow papyrus
-The Rope Stretchers - 61What did the Egyptian papyri have written on them?Practical mathematical questions
- 62What was on the Rope Stretchers painting and where was it found?-Scribes measuring and recording the harvest
-Found in Thebes - 63What is famous secondary source do we have of Egyptian mathematics?Herodutus in 440 BCE
Wrote on how the Pharaoh split the land geometrically - 64What was the culture toward mathematics in Ancient Egypt?They valued math to be for the riches, that being the scribes or higher
- 65What was the culture around being a scribe?-Required special training and this justified their social standing
-People idolized them but not as much as the Pharaoh
-Did calculations and counted inventory for the Pharaoh - 66What is utilitarian mathematics?Practical mathematics with variables to discover as the final solution
- 67What is supra-utilitarian mathematics?Mathematical practical situations but which, without having theoretical pretensions, goes beyond anything which could ever be encountered in real practice
- 68What is special about fractions with the Egyptians?The Scribes only use unitary fractions 1/2, 1/3, 1/4 with the exception of 2/3s.
- 69What were the practical uses of utilitarian mathematics used by the Egyptians and the Mesopotamians?Accounting, land survey, construction, and other practical purposes
- 70—
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- NATS 1920 (Test 1 (First 7 weeks)) Flashcards on Test 1 Review, created by Jonathan Bugeya Miller on 31/10/2018.
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