Four Problems Of Antiquity
Three geometric questions raised by the early Greek mathematicians
attained the status of classical problems in Mathematics. These are:
1.. Doubling of the cube
Construct a cube whose volume is double that of a given one.
2.. Angle trisection
Trisect an arbitrary angle.
3.. Squaring a circle
Construct a square whose area equals that of a given circle.
Often another problem is attached to the list:
d.. Construct a regular heptagon (a polygon with 7 sides.)
The problems are legendary not because they did not have solutions,
or
the solutions they had were unusually hard. No, numerous simple solutions
have been found yet by Greek mathematicians. The problem was in that all
known solutions violated an im****tant condition for this kind of problems,
one condition imposed by the Greek mathematicians themselves:
Valid solutions to the construction problems are assumed to
consist of a finite number of steps of two kinds only: drawing a straight
line through two points with a ruler (or rather a straightedge as no marks
are allowed on the ruler) and drawing a circle with a given center and
radius.
You are referred to solutions of problems #2 and #3 as examples of
existent solutions. That no solution exists subject to the self-imposed
constraints has been proved only in the 19th century.
Doubling the Cube
Doubling the Cube, the most famous of the collection, is often
referred to as the Delian problem due to a legend that the Delians had
consulted Plato on the subject. In another form, the story asserts that
the
Athenians in 430 B.C. consulted the oracle at Delos in the hope to stop
the
plague ravaging their country. They were advised by Apollo to double his
altar that had the form of a cube. As a result of several failed attempts
to
satisfy the god, the pestilence only worsened and at the end they turned
to
Plato for advice.
Problem is, Plato was born in 428 BCE.
No biggee though. Xenophon added 58 years to Greek history, part of that
process involved moving an eclipse from 402 BCE back to 431 BCE. The
original date for the Peloponnesian War was actually 403 BCE when Plato
was
25 years of age. When 30 years were added to the period between the
Persian
and PPW, originally 20, becoming 50, and then the eclipse was pushed back
to
begin the war in 531 BCE instead of 403 BCE, then 58 fake years got added
to
the Greek timeline. Unfortunately, the year of the war now occurs 2 years
before Plato is born, so the Delian Problem doesn't work any more.
Still, this is on the books, uncorrected and historians are clueless that
Xenophon, Plato and Aristotle helped to architect the Greek Period
Expansion.
The 58 years gets adjusted to 52 years, though since 50 is not divisible
by
4 and that affects the Olympic cycle. The PPW has to begin in the 1st
year
of the Olympic Cycle, which it does in either 403 or 431 BCE. But to
establish a 50-year interval between the two wars where there originally
was
just 20 years throws the Olympics off by 2 years. Thus if you add 51 to
431 BCE the Persian War (Battle of Salamis) should fall in 482 BCE. But
that's not an Olympic year. It is well established that Xerxes invaded
during an Olympic year. So that got adjusted down to 480 BCE. Meaning
the
50-year interval doesn't really work from 431 BCE. It's only 48 years
(432+48=480).
The extra 58 years distorts all the chronology back to the time of Solomon
and even back to the Exodus. But RC14 dating and archaeological dating
have
clearly established that Solomon is dated too early. The buildings
ascribed
to Solomon in the Bible were built in the early 10th century. That would
be
the case if Solomon is downdated to the original chronology, 58-60 years
later. Historians are yet to catch on to the revision or to understand
the
Assyrian and NB timelines are basically 50-60 years too early.
Lars Wilson
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