[Today’s class: Number words in various languages worksheets,

Ratio of circumference to diameter activity,

Circle area formulas from various civilizations (some via activities),

Estimates of p in various civilizations,

Archimedes’ estimate of p,

Life and mathematics of Archimedes]

Mathematics 115

Homework Assignment #11

Due Monday, January 28, 2002

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Prof. Beery's office hours this week:           Thursday 1/24   11 a.m.-12:30 p.m., 4-5 p.m.

Friday 1/25   2:30 - 4:30 p.m.

Monday 1/28   10:30 a.m.-12:30 p.m., 4-5 p.m.

and by appointment   Hentschke 203D, x3118

Tutorial sessions:  Sunday 1/27 afternoon, _______ p.m., Hentschke 204 (Jody) and

Monday 1/28 morning, 11 a.m., Hentschke 202 Study Lounge (Sasha)

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Read    from the Mathematics of Ancient Egypt and Mesopotamia section:

"Egyptian Geometry (pages 390-395)

from the Mathematics of Ancient Greece section:

"The Greeks" (pages 404-407: "Archimedes of Syracuse")

"Archimedes' Determination of Circular Area"

Do:    A.  Exercises 2 – 5 from Ratio of Circumference to Diameter handout

B.  Exercises 9, 11, and 13 from page 396 of "Egyptian Geometry"

C.  Estimating the Circumference of a Circle (handout), Parts A (1-6) and B (1-8)

Note: Stop after you've filled in the last blank on the second page.

D.  Exercise 20 from page 410 of "The Greeks."  Let  r = 1.  Remember that you are

estimating the circumference of the circle using the perimeter of each dodecagon

(12-gon), then dividing by the diameter to estimate  π.  Your answer to part (a)

should look familiar.

1.   Archimedes' masterpiece probably has the title, On the Sphere and the Cylinder,

because Archimedes' favorite proposition in it is that the cylinder is "half again"

as large as the sphere in surface area and in volume.  What does Archimedes

mean by "half again"?

2.   On page 104, you are told that the surface area S of a cylinder whose top and

bottom have radius r and whose height is h (such a cylinder is shown in Figure

4.9), is  2πrh + πr2  + πr2.  Which one of the three terms gives the area of the top

of the cylinder?  Which one gives the area of the bottom of the cylinder?  The

remaining term, then, must give the area of the side of the cylinder.  Show that

the remaining term does indeed give the area of the side of the cylinder by

unrolling the side of the cylinder and labeling its edges with the correct lengths.

Monday's quiz will be a 20-point quiz covering Archimedes' life and work, circles, and π.

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