[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)

*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)

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__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)

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* *

__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.

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__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.**

** **

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** **

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

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

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** **

**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.