Mathematics Pre-May Seminar 2 February 2009. Surviving image of Pythia from Delphi.

Mathematics Pre-May Seminar

2 February 2009

Surviving image of Pythia from Delphi

Famous statements of the Oracle: Croesus

• In 560 BC Croesus of Lydia consulted all the famous oracles as to what he was doing on an appointed day. According to Herodotus the oracle proclaimed

– I count the grains of sand on the beach and measure the sea; I understand the speech of the dumb and hear the voiceless. The smell has come to my sense of a hard shelled tortoise boiling and bubbling with a lamb's flesh in a bronze pot: the cauldron underneath it is of bronze, and bronze is the lid.

• Delphi was declared the winner, Croesus asked if he would have a long reign. He was told

– Nay, when a mule becometh king of Medes, flee, soft-soled Lydian, by pebbly Hermus, and stay not, nor feel shame to be a coward.

• Croesus thought it impossible that a mule should be king of the Medes and so asked advice about attacking Persia, and according to Herodotus Croesus was told

– After crossing the Halys, Croesus will destroy a great empire.• Croesus was pleased by the response and attacked the Persians. The defeat of

Croesus ensured that he had destroyed his own empire. He apparently forgot that Cyrus, the victor was in fact half Mede (by his mother), half Persian (by his father) and therefore could be considered a mule.

Famous statements of the Oracle: Persian Invasion

• In 480 BC, when Xerxes the son of Darius of Persia, returned to finish the job of conquering the Greeks in which his father had failed, the Athenians consulted the oracle. They were told– Now your statues are standing and pouring sweat. They shiver with dread. The

black blood drips from the highest rooftops. They have seen the necessity of evil. Get out, get out of my sanctum and drown your spirits in woe.

• It was unambiguous. When persuaded to seek advice a second time the oracle gave a way for the Athenians to escape their doom. Athena had approached her father for help for her city. Zeus said that he would grant that– a wall of wood alone shall be uncaptured, a boon to you and your children.

• The oracle again advised Athenians to flee– Await not in quiet the coming of the horses, the marching feet, the armed host

upon the land. Slip away. Turn your back. You will meet in battle anyway. Oh holy Battle of Salamis, you will be the death of many a woman's son between the seedtime and the harvest of the grain.

Michelangelo’s Delphic Sybil on

the Cappella Sistina ceiling

Cappella Sistina in the

Vatican

Cappella Sistina toward Michelangelo’s Last Judgment

Last Judgment, Duomo, Firenze

The Moscow Papyrus: Frustum of a Pyramid

• The Moscow papyrus contains only about 25, mostly practical, examples. The author is unknown. It was purchased by V. S. Golenishchev (d. 1947) and sold to the Moscow Museum of Fine Art. Origin: 1700 BC. It is 15 feet long and about 3 inches wide.

• Problem 14. Volume of a frustum. The scribe directs one to square the numbers two and four and to add to the sum of these squares the product of two and four. Multiply this by one third of six. "See, it is 56; your have found it correctly."

• What the student has been directed to compute is the number

• V=(1/3)*6(2^2+2*4+4^2)=56

• Here's the picture that is found in the Moscow Papyrus.

Image of Problem 14

from the Moscow Papyrus

Volume of the Frustum from Problem 14

Calculating the volume using Calculus:

USA’s Great Seal, Reverse