Mathematics in Western Civilization
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Mathematics in Western Civilization

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Questions and Answers

What was the term used by certain Australian aboriginal tribes for any number larger than two?

  • Many (correct)
  • Much (correct)
  • Several
  • Few

    • What number system did the South American Indians along the Amazon use for groups larger than two?

  • Standard counting
  • Descriptive phrases (correct)
  • Roman numerals
  • Binary code

    • Up to what number could the Bushmen of South Africa count using only two words?

  • Eight
  • Ten (correct)
  • Twelve
  • Five

    • What method was primarily used by early humans to visibly express the idea of number?

    <p>Tallying</p> Signup and view all the answers

    When counting sheep, what was used as a tool to keep track of the count?

    <p>Pebbles</p> Signup and view all the answers

    What phrase did the South American Indians use to indicate the number four?

    <p>Two-two</p> Signup and view all the answers

    How did tribal groups typically perform trades involving larger numbers?

    <p>By simple exchanges</p> Signup and view all the answers

    What physical structure was often erected to symbolize victory, a treaty, or village founding?

    <p>Cairn</p> Signup and view all the answers

    What would the reappearance of either a figure-eight or long knot indicate?

    <p>Another number is recorded on the same cord.</p> Signup and view all the answers

    What does an empty position on a cord represent?

    <p>A value of zero.</p> Signup and view all the answers

    How many twists are in the long knot mentioned in the example?

    <p>Four twists.</p> Signup and view all the answers

    What was a significant cultural achievement of the ancient Maya?

    <p>Development of an elaborate hieroglyphic writing system.</p> Signup and view all the answers

    What is one of the primary aims of the book discussed in the content?

    <p>To provide an explanation of mathematics' cultural significance</p> Signup and view all the answers

    During which period did the Mayan civilization reach its peak?

    <p>300-900 A.D.</p> Signup and view all the answers

    Which notable figure's efforts in American mathematics is highlighted in Section 12.1?

    <p>Robert Adrain</p> Signup and view all the answers

    What happened to the Mayan civilization around 900 A.D.?

    <p>They experienced a sudden decline.</p> Signup and view all the answers

    How many glyphs does the elaborate writing system of the ancient Maya use?

    <p>About 1000 glyphs.</p> Signup and view all the answers

    What significant addition was made in the seventh edition of the book?

    <p>Enhanced treatment of American mathematics</p> Signup and view all the answers

    Which of the following mathematicians was NOT mentioned in relation to American mathematics?

    <p>Henri Poincaré</p> Signup and view all the answers

    What does the array of knots on a cord translate to in terms of place value for the Inca?

    <p>$17024$.</p> Signup and view all the answers

    What does the author express gratitude towards at the beginning of the content?

    <p>The scholarship of others</p> Signup and view all the answers

    Which of the following individuals is associated with observational astronomy in relation to mathematics?

    <p>George William Hill</p> Signup and view all the answers

    What aspect of the book remains unchanged from previous editions?

    <p>The overall organization and content</p> Signup and view all the answers

    Which of the following individuals is an example of a more recent mathematician discussed?

    <p>Walter Feit</p> Signup and view all the answers

    What was the method used by the Egyptians for addition?

    <p>Converting numbers to symbols and combining them</p> Signup and view all the answers

    How did the Egyptians perform subtraction?

    <p>Using addition principles with borrowing</p> Signup and view all the answers

    What was the primary reason for the invention of papyrus by the Egyptians?

    <p>To have a cheaper and accessible writing material</p> Signup and view all the answers

    What do the hieroglyphs used for addition and subtraction resemble?

    <p>Human legs in motion</p> Signup and view all the answers

    What limitation existed regarding Egyptian writing before papyrus?

    <p>Restricted to short, important inscriptions</p> Signup and view all the answers

    How did Egyptians indicate mathematical operations in their writings?

    <p>Through symbols resembling their mathematical concepts</p> Signup and view all the answers

    What did the Rhind Papyrus represent?

    <p>Methods of Egyptian addition and subtraction</p> Signup and view all the answers

    What was the significance of the symbol for a large number in Egyptian subtraction?

    <p>It was exchanged for lower-order symbols</p> Signup and view all the answers

    What was the primary material used for creating ancient writing surfaces?

    <p>Papyrus</p> Signup and view all the answers

    Which process was used to bond the sections of papyrus together?

    <p>Soaking and pounding</p> Signup and view all the answers

    Which script developed from hieroglyphics was characterized by a cursive style?

    <p>Hieratic script</p> Signup and view all the answers

    What was the primary advantage of Egypt's climate for the preservation of scrolls?

    <p>Dry climate</p> Signup and view all the answers

    What substance was typically used to make the ink for writing on papyrus?

    <p>Colored earth or charcoal</p> Signup and view all the answers

    Which script is described as a form of shorthand and emerged after the hieratic script?

    <p>Demotic script</p> Signup and view all the answers

    What was the typical width range of finished papyrus sheets?

    <p>10 to 18 inches</p> Signup and view all the answers

    What was the appearance of sections of papyrus after being processed?

    <p>Coarse and brown</p> Signup and view all the answers

    Study Notes

    Mathematics in Western Civilization

    • Mathematics has become a pivotal cultural force in Western civilization, leading to extensive scholarship and exploration in its history.
    • The seventh edition of a significant work maintains the organization and content of previous editions but includes several improvements.

    American Mathematics Contributions

    • Enhanced treatment of notable American mathematicians: Robert Adrain, Benjamin Banneker, Simon Newcomb, George William Hill, Albert Michelson, and Maria Mitchell.
    • The historical context includes the role of mathematicians as observational astronomers in the 19th century.

    Primitive Counting Systems

    • Certain tribal groups have limited counting systems; for example, some Australian Aboriginal tribes count only to two, referring to larger numbers as "much" or "many."
    • South American Indians also had a limited counting vocabulary, using phrases like "two-one" for three and "two-two" for four, not having unique names for three through six.

    Early Number Representation Techniques

    • The tallying method visually matched collections to be counted with easily accessible objects, such as fingers or stones.
    • A practical counting example: during sheep gathering, a pebble was used for each counted sheep, demonstrating early numerical accounting.

    Inca and Mayan Numeration Systems

    • Inca culture utilized a place value system on cords, recognizing empty positions as zero and using a combination of knots for representation.
    • The Mayan civilization thrived between 300-900 AD and developed an intricate system of hieroglyphic writing with around 1000 glyphs, many of which are undeciphered.

    Egyptian Numerical Methods

    • Egyptian hieroglyphs represented numbers but lacked uniform notation for arithmetic operations.
    • The Rhind Papyrus (circa 1650 B.C.) includes symbols for addition and subtraction akin to human figures.

    Papyrus and Egyptian Writing

    • Egyptians created papyrus sheets from the papyrus plant, allowing longer records than stone inscriptions.
    • The durability of papyrus, coupled with Egypt's dry climate, preserved numerous scrolls.
    • Egyptian priests developed a quicker, hieratic script for writing that evolved into the even faster demotic script, reflecting advancements in written communication.

    Historical Significance

    • The transition from pictorial writing to cursive and shorthand forms illustrates the evolution of mathematical and written expressions over centuries, linking mathematics with cultural and practical advancements.

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    Description

    Explore the significant role of mathematics as a cultural force in Western civilization. This quiz covers the contributions of notable American mathematicians and the historical context of primitive counting systems found in various tribes. Test your knowledge on how these aspects have shaped mathematical scholarship and exploration.

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