MTH 441 Historical Perspectives in Mathematics Assignments

• Responses to Presentations -- an ongoing assignment which will start in two weeks.   On 1/27 we will begin having student presentations.   Remember to see me one week before your presentation!  Response to Presentations -- Due from each class member other than the presenter(s) within 4 days of the presentation is an email message to me commenting constructively on the presentation using the  peer comment template    (Download, complete, and attach to email message to me).  Include what you feel worked particularly well as well as any suggestions for improvement Use the grade sheet for a guide for criteria for comments.  These will be collated and sent (without names) to the presenters.
  

  Due Date	Assignment
  Tues 01/13	In-class assignment:  Creating your electronic journal using Introductory Page on Creating and Publishing Web pages. Select partners, topic, and date for first presentations -- see Greek Partner Presentations.
  Thurs. 01/15	At the web site The MacTutor History of Mathematics Archive   Select the History Topics Index  -- read  1. Overview of the History of  Mathematics and  2. Ancient Egyptian Mathematics --  Part 1:  An Overview of Ancient Egyptians Mathematics. Then write a short essay  (1 page typed in Word or html)  on the following,  based on your readings: Briefly describe the history of Ancient Egypt, including time period,  geographical region,  and historical factors that contributed to the flourishing of the civilization's culture.  Place a link to the essay in your electronic journal (or if you do not have the journal page up and running yet, email as an attachment to me.) In class assignment (we will do together in class):   Equation Editor Practice
  Tues 01/20	At the web site The MacTutor History of Mathematics Archive   Select the History Topics Index -- Select History Topics Index  -- read  Ancient Egyptian Mathematics --  Part 2.  Egyptian Papyri  and Part 3.  Egyptian Numerals.
  Thurs 01/22	Reading: At the web site The MacTutor History of Mathematics Archive   Select the History Topics Index -- Select History Topics Index  --  Babylonian  Mathematics -- Read  Part 1.  Overview of Babylonian Mathematics and Part 2.  Babylonian Numerals. Go to the link  Mesopotamian Mathematics  and choose the link on Quadratic Equations under Special Topics. In-class exercise (time permitting):  Identify what is wrong with the mathematical notationin each of the examples in Bad Examples.  Use Writiing Guidelines  as a reference. Written Exercises on Egyptian Arithmetic. Write out by hand and turn in at beginning of class. E1.  Write each of the following numbers in Egyptian hieroglyphics: a)  1234 b)  1,240,307 c)   1/123 E2.  a)  Write the following two numbers in hieroglyphics and then add using hieroglyphics.  Express the answer in  hieroglyphics, then translate to our number system.       678 + 345.  b)  Write the following two numbers in Egyptian hieroglyphics, subtract the second from the first , then translate to our system.      2631 - 642 E3.  Use the Egyptian method of multiplication by doubling to compute the following products: a)  26 * 33 b)  17 * 21 E4.  Use the Egyptian method of division to compute the following divisions: a)  184 / 8 b)  27 / 8
  Tues 01/29	Reading: Handout on Writing Mathematics. Web page assignment: The Moscow and Rhind Papyri. ( Place a link to this paper on your electronic journal web page for this class.) On the Internet  and/or in printed resources, find information about these papyri.   Write a description (on a  web page)  (approximately 1 page).   Include in your information for each  -- when they were discovered, a  picture or link to a picture of part of the contents of each papyrus on the page, an example of what is contained on the papyri,  and why they are important -- plus anything else you find interesting about them. Cite your references.   Then include discussion of the following problems: 1.  Problem 10 of the Moscow Papyrus computes the surface area of a hemispherical basket of diameter d = 4 + 1/2 to be   (1 - 1/9)2 *(2d)*d. Show that if we use Pi as 4*(8/9)2, the correct formula:  Pi * d2 /2 results. You can go to this link:   EGYPTIAN GEOMETRY - Mathematicians of the African Diaspora to get a line by line translation of the problem. 2.  Find a problem from either the Moscow Papyrus or the Rhind Papyrus that we have not discussed.   Discuss the problem and the solution formula represented by the problem Cite the source of your problem. ( To receive a better than average grade on this you must give clear and complete explanations, going beyond the minimum requirements.  For the problems, start with a statement of the problem.  Then give a mathematically clear and correct explanation. ) Written Homework Exercises: B.1.  Write each of the following numbers in base 60 form and then cuneiform notation.       1234       23561 B.2.  Convert the following numbers from base 60 (sexagesimal) to decimal:      2, 31, 45      2, 12; 12 B.3.   Find via search through references or the Internet suggestions of why the Babylonians might have used base 60 for their number system. B.4.  Discuss the advantages of the Babylonian number system over the Egyptian number system. B.5.  Translate the approximations in ;8, 34, 16, 59 < 1/7 < ;8,34, 18 to base 10 and then compare their accuracy to the value of 1/7. B.6. Express the numbers in the following problem in sexagesimal notation -- then compute the division using the method of multiplying by the reciprocal  (also write down the reciprocal first in sexigesimal notation.   Then convert to a fraction in our notation. a)  31 / 15 b)  49 / 12 B.7. In a manner somewhat similar to the in class exercise,  solve the following Babylonian problem by getting obtaining a quadratic only in (x-y).   x + y = 50, x2 + y2 + (x-y)2 = 1400.  Hint:  Subtract the square of the first equation from twice the second equation, again to get a quadratic in x-y.
  Thurs 1/31	Web page assignment: Babylonian Geometry:  Plimpton 322 Tablet On the Internet  and/or in printed resources, find information about this tablet.  Write a description (on a  web page)  (approximately 1 page).   Include in your information when it was discovered, a  picture or link to a picture of the tablet on the page, what is contained on the tablet,  and why it is important.  Cite your references. Place a link to this paper on your electronic journal web page for this class.
  Tues 2/24	Reading:  Read class discussion notes on the Decline and Revival of Mathematics as well as the referenced web sites in that discussion. If not completed in class, submit by Thursday February 26th Exercise:  Use the method indicated in the article at Mac-Tutor site:  Al-Khwarizmi.on the following: x2 + 5x = 36. Do it both algebraically and geometrically (provide the drawing).  (Turn in as written assignment.)    Post to web page by Thursday March 4th Exercise: After reading the  MacTutor History of Mathematics article on Leonardo Pisano  Fibonacci, write a short summary of his life and discuss one of his mathematical results (other than the Fibonacci numbers)  in some detail (within a web page).  (The result can be from this article or another that your find -- please cite).  Place a link to your article on your Historical Persepctives web page.