[Today’s class: Circles, continued,

Archimedes, continued,

Perimeter versus area, including legend of Queen Dido,

Indian mathematics, including worksheets on what we would call algebra problems]



Mathematics 115

Homework Assignment #12

Due Tuesday, January 29, 2002


We do not listen with the best regard to the verses of a man who is only a poet,

nor to his problems if he is only an algebraist; but if a man is at once acquainted

with the geometric foundation of things and with their festal splendor, his poetry

is exact and his arithmetic musical. – Ralph Waldo Emerson (1803-1882)


Many people who have never had occasion to learn what mathematics is confuse it with

arithmetic and consider it a dry and arid science.  In actual fact it is the science which demands the utmost imagination.  One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit. . . . It seems to me that the poet must see what others do not see, must see more deeply than

other people.  And the mathematician must do the same. – Sonya Kovalevskaya, 1890


It is true that a mathematician, who is not somewhat of a poet, will

 never be a perfect mathematician. - Karl Weierstrass (1815-1897)


Pure mathematics is . . . the poetry of logical ideas. - Albert Einstein (1879-1955)



Prof. Beery's office hours this week:            Monday 1/28   10:30 a.m.-12:30 p.m., 4-5 p.m.

                                                                  Tuesday 1/29   10:30 a.m.-12:30 p.m., 4-5 p.m.

                                                             Wednesday 1/30   10:30 a.m.-12:30 p.m., 4-5 p.m.

                                                                 Thursday 1/31   10:30 a.m.-12:30 p.m.

                                                         and by appointment   Hentschke 203D, x3118

Tutorial sessions this week:       Tuesday, Wednesday, and Thursday mornings, 11 a.m.,

                                                Hentschke 202 Study Lounge (Sasha)



Read:   "The Fibonacci Sequence"

            "Now and Then:  Fiber Meets Fibonacci / The Shape of Things to Come"

            "Maria Gaetana Agnesi"

            "Sophie Germain"

            "Sonya Kovalevskaya"

            These readings are in the Mathematics of Europe section (beginning and end). 


Do:    From "The Fibonacci Sequence" Exercises, do Set I, Set II, and Set III, skipping

         only Exercise 15 from Set II.  In Exercise II.13, round off to 4 places after the

         decimal point.  What is the name of the special number the ratios are approaching?

         From "Golden Explorations" (at the end of the "Now and Then" reading), do

         only Golden Exploration 1, but read the others!

         You may do the assignment on notebook paper or directly on the handout,

         whichever you prefer.



Looking ahead


For Tuesday's class, please bring scissors, and also colored pencils, pens, or markers, if you have them.


Tuesday's quiz will be a 20-point quiz covering today's class, reading, and homework.


[Tuesday’s class: Four Color Theorem activity,

poetry (and mathematics) of Omar Khayyam,

more on Fibonacci numbers and Golden Ratio,

Platonic Solids and Euler’s Formula activity,

Topology activity: Moebius strips and beyond,

assignment of review problems for presentation in class Wednesday]


Wednesday's quiz will be a 10-point quiz covering completing the square.


For Wednesday's class, you and your team will prepare assigned review problems for presentation to the class.  You'll have time at the start of class to write your problems and their solutions on the board or on transparencies.


Final Quiz (100 points), Thursday, Jan. 31, 1 – 3:50 p.m.




Just for fun:        The numbers  6, 28, and 496  are called perfect numbers.  Why? 

                            (Hint:  Sum the proper divisors of each number.)



For even more fun:    Multiply the number  142857  by  2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, . . . 

                                    What happens? 

                                    Explain how multiplication by 8 fits the pattern. 

                                    What about multiplication by 9? 

                                    Note:    Multiplying  142857  by successive integers is the same as

                                                adding  142857  to itself repeatedly.


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