# Hipparchus I

## A Mathematics Problem Book

January 2003

#### Hipparchus 1 is the third of a series of books of mathematics problems, largely invented by its author.

It contains 17 problems at the level of graduate students and advanced undergraduates in mathematics. It is the author's hope that some of these problems are challenging to mathematicians in general.

All solutions are written out in full.

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Hipparchus of Nicea (200 AS (After Socrates)) enjoyed legendary fame as an astronomer in the Ancient World. Although most of his writings ae lost, it is known that Ptolemy drew heavily on his star catalogues in the production of the Almagest

Hipparchus is also considered by some to be the inventor of Trigonometry. His Tables of Chords was essentially a table of sines and cosines.

He invented the "four cubit rod dioptra", an early astonomical instrument for masuring, to a high degree of accuracy in an age without telescopes, the angular position of stars. He discovered the precession of the equinoxes, that is to say the 26,000 year cycle of rotation of the Earth's polar axis to the plane of the Ecliptic.

### Problems

### 1-4:Diophantine Equations

5-7: Special Relativity

8-12: Integer Points on Polynomial Curves

13-17: Sums of Cubes over Algebraic Number Fields

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The price of "Hipparchus I" is $15

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Send check, cash or money order to:

Roy Lisker

8 Liberty Street#306

Middletown,CT 06457

rlisker@yahoo.com