Mathematics PreMay Seminar

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Mathematics Pre-May Seminar

• 2 February 2009

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Surviving image of Pythia from Delphi
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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.

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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.

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Michelangelos Delphic Sybil on the Cappella
Sistina ceiling
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Cappella Sistina in the Vatican
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Cappella Sistina toward Michelangelos Last
Judgment
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Last Judgment, Duomo, Firenze
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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(222442)56
• Here's the picture that is found in the Moscow
  Papyrus.

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Image of Problem 14 from the Moscow Papyrus
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Volume of the Frustum from Problem 14
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Calculating the volume using Calculus
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USAs Great Seal, Reverse