Mathematician Dido

Peter Oye Sagay

Jul 27, 2018

Dido was a great historical and mythical figure. She was the daughter of King Bellus II of Tyre (in modern Lebanon). Dido founded ancient Carthage (modern city of carthage is a suburb of Tunis, Tunisia) about 814 B.C after she left the kingdom of Tyre with an entourage because of palace intrigue with his brother. In Carthage, she was Queen Elissa, or simply Dido. Carthage flourished under Dido's reign. She was a great space pioneer and leader, a humanitarian, and a great mathematician.

As a humanitarian, she made ancient Rome possible when she harbored and cared for Aeneas and his compatriots who were marooned refugees from Troy. Aeneas was the progenitor of the founders of Rome. Dido's brilliance did not shine long enough. She killed herself for love. Aeneas who was her love interest refused to permanently remain with her in Carthage. He was in pursuit of his own destiny. What a destiny that became. The Rome that the descendants of Aeneas founded became a great empire. The Great Roman Empire had several African connections. For example, the famous Rome-Egypt connection during the reigns of Julius Caesar, Anthony and Queen Cleopatra VII. However, the Dido Connection is the greatest because it was fundamental. Had Aenas died at sea, Rome may not have been founded. Perhaps it would have been founded by others with a different descent linage. What Rome would that have been? Greater than the Roman Empire that was, or just a little town in some country side? We will never know. What we know is that Aeneas gave the world a Great Roman Empire and Dido's help influenced the sequence of events that led to that greatness. Unfortunately, Carthage and Rome became historical enemies. Oh what a tangled web descendants weave.

As a brilliant mathematician, Dido was the first person to determine that given a fixed amount of fencing (i.e., a given perimeter), the maximum area that can be enclosed along a river front, if no fencing is required along the shore itself, is a semicircle. After she made an agreement to pay a definite sum of money for as much land as "could be encompass by a bull's hide", Dido took a bull's hide, cut it up into thin long strips, strung the strips together, and used the length to demarcate a land space. She chose an area along the shore, because she knew that no hide would be needed along the shore. She then determined that the maximum area the bull's hide can enclose is a semicircle. She demarcated the space and founded Carthage by the Mediterranean sea.

Consider figure 1a. Let the curve ABC represents Dido's bull's hide and the line AC the shoreline under consideration. The objective of Dido was to determine the shape of ABC that would encompass maximum land space. Dido decided that a semicircle was the most favorable shape. Dido was right.

Now, let us use figure 1b to prove Dido's correctness. Figure 1b is obtained by enclosing an area on both sides of AC with twice the length of hide Dido used for one side. The problem then reduces to determining the maximum area which can be completely enclosed by a perimeter of a specific length. The answer to this problem is a circle. Consequently, arc ABC which encloses maximum area on one side of AC (the shoreline) must be a semicircle. If arc ABC is different from a semicircle, it would, together with its mirror image in AC, enclose a larger area than the circle and yet have the same perimeter as the circle. An impossible scenario.

Dido, the great Queen of ancient Carthage, a great humanitarian and a great mathematician. She probably had other beautiful traits worth emulating. The 1st Earl of Mansfield was one of the people who thought so. The movie Belle (a film about a biracial young woman who lived in the times of the distinguished writer, Jane Austen) premiered several years ago. Belle was written by pediatrician and screen writer Misan Sagay and directed by Asante. It is believed that Earl Mansfield, 1st Earl of Mansfield, nicknamed the main character of the film Elizabeth Dido (played by Mbutha Raw) after Queen Dido of Carthage. One wonders which of the great talents of Queen Dido, Earl Mansfield observed in Belle.

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