Eratosthenes of Cyrene (276-194 BC). Finding Earth’s Circumference. January 21, 2013 Math 250. Eratosthenes’ Method. Results of Eratosthenes.
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Eratosthenes of Cyrene(276-194 BC)
Finding Earth’s Circumference
January 21, 2013
23° 51' 15", prepared a star map containing 675 stars, suggested that a leap day be added every fourth year and tried to construct an accurately-dated history.
Hipparchus-Ptolemy Models for Planetary Orbits
The following equation represents the circular motion of a planet, P around the Earth, E.
= radius of orbit
= phase parameter
P at z1(t)
This equation demonstrates the observed retrograde motion of a planet as seen from Earth. The planet, P, undergoes uniform circular motion about a point that undergoes uniform circular motion about the earth, E.
P at z2(t)
Connection to Fourier Series
Note: Only a truncated Fourier Series if
are all rational numbers.
Hipparchus-Ptolemy Model Using Cartesian Coordinates