Queen Dido Activity

According
to the Roman poet Virgil’s epic poem, the *Aeneid,* Princess Dido, the
daughter of the king of the ancient Phoenician city of Tyre,
fled Tyre after her brother, Pygmalion, murdered
her husband. She ended up in what is now Tunisia on the Mediterranean coast of
Africa, where she agreed to pay a certain sum of money for as much land as she
“could enclose with one bull’s hide” (Fitzgerald, *Aeneid,* Book I, 16).
Dido then took a bull’s hide, cut it up into long, thin strips, tied the strips
together end-to-end, and set out to enclose the largest amount of land
possible. She chose land along the sea, so that she could use the shoreline as
one edge of her enclosure. She still needed to decide in what shape to lay the
bull’s hide in order to enclose the largest area possible (Kline, 134-135;
Perl, 72-73).

Your assignment: Using the edge of your desk as the coastline and a 12” piece of string as the bull’s hide, form different shapes and compute their areas. Sketch each shape you create and be sure to record its area. Which shape has the largest area? In what shape should Dido have laid the hide in order to enclose the largest area possible?

According
to the *Aeneid,* the land Dido purchased became the great city of Carthage and
Dido herself became its queen. Unfortunately, Queen Dido did not live to
perform many more mathematical feats. Not too many years after she founded Carthage, the
mythical Trojan hero Aeneas blew into town. Dido fell in love with Aeneas and
begged him to stay. When he refused, Dido threw herself on a sword Aeneas had
left behind, committing suicide (Fitzgerald, *Aeneid,* Book IV, 119-121).
Again according to the *Aeneid,* Aeneas went on to fulfill his destiny by
settling in what is now Italy, where his descendants would found the
city of Rome. The historical city of Carthage
flourished from the ninth century BCE until 146 BCE, when it was destroyed by
the Romans.

Instructor Notes

Objective: Students will compare the areas of shapes with the same perimeter. They should conclude that, among shapes formed using a straight “coastline” as one edge and a string of fixed length for the remaining edge(s), the semicircle has the largest area.

Materials: Provide each pair of students with a 12” string, a ruler, and 1/4-inch graph paper.

How to Use: Students should compute areas of several different shapes, working individually or in pairs. You might suggest shapes for the students to try, such as triangles, rectangles, pentagons, hexagons, circles, or irregular shapes. Students could use any or all of the following methods for finding the areas:

1. Use a formula to find the area of the region.

2. Divide the region into smaller shapes whose areas are known and sum the areas.

3. Use grid paper and count the squares to approximate the area as closely as possible.

You might direct students to calculate areas using a specific method, or you might let them experiment and come up with methods of their own. For each shape they try, students should provide a sketch and record the total area.

Solution: Among shapes formed
using a straight coastline as one edge and a string or rope of fixed length for
the remaining edge(s), the semicircle has largest area. Therefore, Dido should
have laid her cowhide strips in the shape of a semicircle. A semi-circle formed
from a 12” string has radius _{} (since _{}) and area _{} square
inches.

**Background
Information: **The Roman
poet Virgil (70-19 BCE) wrote his famous epic poem, the *Aeneid,* during
the last ten years of his life. He modeled the *Aeneid* on the *Iliad*
and especially the *Odyssey,* the well-known epic poems of the much
earlier Greek poet, Homer (*c.* 750 BCE). In the *Iliad, *Homer* *tells
the story of the Trojan War, fought in Troy between the Greeks and the hometown
Trojans; in the *Odyssey,* he recounts the adventures of Odysseus, a hero
of the Trojan War on the winning Greek side, during his circuitous ten-year
journey home to Ithaca after the war. In the *Aeneid,*
Virgil’s protagonist, Aeneas, also a hero of the Trojan War despite having been
on the losing Trojan side, flees Troy after the city is destroyed with a band
of loyal followers. As they wander about the Mediterranean,
he and his men have a series of hair-raising adventures until, finally, Aeneas
is able to fulfill his destiny by settling in Italy
where his descendants will found Rome.

**References: **Activity from *Lengths, Areas, and
Volumes, *by J. Beery, C. Dolezal, A. Sauk, and L. Shuey, in *Historical
Modules for the Teaching and Learning of Secondary Mathematics,*
Mathematical Association of America, Washington, D.C., 2003.

Fitzgerald,
Robert (translator), *The Aeneid of Virgil, *Random House, New York, 1990.

Kline, Morris, *Mathematics
for Liberal Arts,* Addison-Wesley, Reading, Massachusetts, 1967.

Perl, Teri, *Math
Equals,* Addison-Wesley, Menlo
Park, California, 1978.

** **