[Today’s class:  Sieve of Eratosthenes activity,

Heron, Diophantus, Hypatia,

Geometric algebra, including algebraic identities, square root computation in China, one more proof of Pythagorean Theorem, and completing the square, 

Mathematics of Middle Ages, especially of Arab Empire]



Mathematics 115

Homework Assignment #10

Due Thursday, January 24, 2002




Prof. Beery's office hours:             Wednesday 1/23      4 – 5 p.m. (Sorry!)

                                                        Thursday 1/24      11 a.m.-12:30 p.m., 4-5 p.m.

                                                            Friday 1/25      2:30 - 4:30 p.m.

                                                and by appointment      Hentschke 203D, x3118

Tutorial sessions:  Thursday 1/24 morning, 11 a.m., Hentschke 202 (Sasha)



Read:   "Heron's Formula for Triangular Area" (Eratosthenes, Apollonius, Heron,

                  Ptolemy, Mohammed ibn Musa al-Khowarizmi, Tabit ibn Qorra)

            "Hypatia"  (These are the last two readings in the Math of Ancient Greece section.)

            "Cardano and the Solution of the Cubic" (Mathematics of Europe section)


Do:    A.  Algebra in Classical Greece worksheet (handout from class)


         B.  Algebra in the Middle Ages worksheet (handout from class)


         C.  Solve for  x  in the equation  x2 + 6x = 16  by completing the square as shown

         in class today.  Use Steps 1 - 4 as demonstrated in class.  You should get two

         solutions,  x = -8  and  x = 2.  Then draw a picture of the completed square

         corresponding to the problem (as shown in class).


         D.  Answer the following questions about "Heron's Formula for Triangular Area."

         1.   Use the quadratic formula to solve the quadratic equation  3x2 + 2x - 5 = 0.

               (Hint:  See page 130!)

         2.   How did "Dark Age" Europeans eventually acquire the mathematical knowledge

               of ancient Greece and of the Arab empire?  Be sure to include what author

               William Dunham describes as the more significant conduit for this knowledge 

               as well as the less significant conduit.


         E.  Answer the following question about "Cardano and the Solution of the Cubic."

         Why did fifteenth and sixteenth century Italian mathematicians keep their

         mathematical discoveries secret?



Thursday's quiz will be a 20-point quiz covering activities from today’s (Wednesday’s) class, and the reading and homework from this assignment (Assignment #10).  This includes being able to tell me stories about Hypatia, and about Cardano and Tartaglia. 


For Thursday's class, please bring a ruler.


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