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.
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.