MAT 300

Spring 2004                               Answers to E-mail Assignements

 

EA1 EA2 EA3      
           

 

E-mail Assignment 1

 

a.       When was the Rhind Mathematical Papyrus written (copied) and who was the scribe that copied it?

The Rhind Papyrus was copied by the scribe A'h-mose ( or Ahmes) in about 1650 BCE from an original about 200 years older.

 

b.   The Egyptians recorded their mathematics on papyrus.  We write on paper.  What medium did the Mesopotamians (Babylonians) of the Hammurapi era use for recording their writing and mathematics (i.e. what did they "write on")?

The Mesopotamians of the Hammurapi era wrote on clay tablets.

 

 

E-mail Assignment 2

  1. In the Rhind Papyrus, the method of false position is used to solve what kind of equations?

    In the Rhind Papyrus the method of false position was used to solve problems involving linear equations, or at least problems involving processes that are equivalent to linear equations.
     

  2. What does the Egyptian term pesu refer to in the Rhind and Moscow papyri?  You will need a phrase or sentence to answer this question.

    Pesu is the Egyptian measure for the inverse "strength: or inverse "concentration" of bread (and other foods made from grain).  Pesu can be expressed as pesu = [number of loaves]/[number of hekats of grain].
     

  3. The Rhind and Moscow papyri have problems involving the pesu of two "foods"  made from grain.  What are those two "foods"?

    The two foods for which I was looking are bread and beer.
     

  4. What does the Egyptian term seked refer to?

    The term seked refers to the slope of the sides of a pyramid, expressed as the number of horizontal units to one vertical unit of rise.   Note that this is the reciprocal of what we consider slope as "rise/run".
     

E-mail Assignment 3

The answers to the following questions should be emailed to me by 2:00 pm on Tuesday, February17.   The answers are all in the reading in the course text.

  1. What numbers are characterized by the author of our text as regular sezagesimal numbers?

    Regular sexagesimal numbers are numbers whose reciprocal is a terminating sexagesimal fraction.
     

  2. How did the Babylonians do the equivalent of our operation of division?

    To divide by a number A, the Babylonians multiplied by the reciprocal 1/A, expressed (or approximated) as a corresponding sexagesimal fraction.
     

  3. Give one way that the Babylonians would have found the area of a circle.  While we might think in terms of formulas, the Babylonians would have thought in terms of procedures or processes.

    One way in which the Babylonians found the area of a circle was to square the circumference and then multiply the result by 1/12 = 0;05 (which is equivalent to dividing the result by 12 ).
     

  4. Plimpton 322 is a tablet in the Plimpton Collection at Columbia University.  In the text's discussion of Plimpton 322, which column does not actually appear on the tablet?

    In the book's discussion of Plimpton 322, the column that does not appear on the tablet is the column on the far right, labeled y.

 

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Last updated:  March 8, 2004