be an integral part of a formal education elevates the
status of mathematics within the Western world.
ca. 386
B
.
C
.
E
.
The oracle of Delos tells the people of Athens that in
order to end a plague they must double the size of the
cube-shaped altar to the god Apollo. This establishes
the problem of
DUPLICATING THE CUBE
.
ca. 370
B
.
C
.
E
.
E
UDOXUS OF
C
NIDUS
(ca. 400–350
B
.
C
.
E
.) develops a
“method of exhaustion” to determine the areas of sim-
ple curved figures. The method is a precursor to the
notion of
LIMIT
developed in 18th-century
CALCULUS
.
ca. 350
B
.
C
.
E
.
A
RISTOTLE
(ca. 384–322
B
.
C
.
E
.) analyzes the structure
of
ARGUMENT
s and logical reasoning to develop ideas
seminal to the field of
FORMAL LOGIC
.
ca. 310
B
.
C
.
E
.
Ruler Ptolemy Soter founds the Library of Alexandria.
It remains the center of intellectual learning for more
than 700 years.
ca. 300
B
.
C
.
E
.
Greek geometer E
UCLID
summarizes all mathematical
knowledge known at his time in T
HE
E
LEMENTS
. The
method of logical deduction and rigor he provides
remains the paradigm of mathematical thinking today.
ca. 240
B
.
C
.
E
.
A
RCHIMEDES OF
S
YRACUSE
(ca. 287–212
B
.
C
.
E
.) uses
the method of exhaustion to compute the area under a
section of a
PARABOLA
. He also makes fundamental
contributions to the fields of geometry, engineering,
astronomy, and hydrostatics. He discovers a method of
computing the value πto any degree of accuracy and
shows, in particular, that its values lies between 3
10/71 and 3 1/7.
ca. 230
B
.
C
.
E
.
E
RATOSTHENES OF
C
YRENE
(ca. 275–195
B
.
C
.
E
.) calcu-
lates the circumference of the E
ARTH
to be 28,500
miles. He develops the
SIEVE OF
E
RATOSTHENES
for
computing
PRIME
numbers.
ca. 220
B
.
C
.
E
.
A
POLLONIUS OF
P
ERGA
(ca. 262–190
B
.
C
.
E
.) develops
the study of
CONIC SECTIONS
. He also develops a the-
ory of
EPICYCLE
s to model planetary motion.
ca. 214
B
.
C
.
E
.
Construction begins on the Great Wall of China.
ca. 150
B
.
C
.
E
.
Hipparchus of Nicaea (ca. 190–126
B
.
C
.
E
.) develops
beginning ideas in the theory of
TRIGONOMETRY
. He
uses geometry to calculate the distances of the Sun and
the Moon from the Earth.
ca. 100
B
.
C
.
E
.
Chinese scholars write J
IUZHANG SUANSHU
(Nine
chapters on the mathematical arts). The text includes
solutions to linear and
QUADRATIC
equations, the com-
putation of areas and volumes, a statement of
P
YTHAGORAS
’
S THEOREM
, and the use of
NEGATIVE
NUMBERS
.
ca. 140
Greek astronomer C
LAUDIUS
P
TOLEMY
writes the
Almagest, the most influential work in mathematical
astronomy until the 16th century. It includes a table of
chord values equivalent to a modern-day table of sines.
He uses the value 377/120 for π.
ca. 250
Greek mathematician D
IOPHANTUS OF
A
LEXANDRIA
writes Arithmetica. He is the first to use symbols to
represent unknown quantities.
ca. 320
P
APPUS OF
A
LEXANDRIA
attempts to revive interest in
the classical Greek pursuit of mathematics. He writes
Synagoge (Collections) as a guide to the great Greek
works.
ca. 370
H
YPATIA
(ca. 370–415), the first woman named in the
history of mathematics, is born. She becomes head of
the Platonist school in Alexandria.
ca. 475
Indian astronomer and mathematician A
RYABHATA
(ca. 476–550) is born. He develops methods for
extracting square roots, summing arithmetic series,
and computing chord values. He uses the value
3.1416 for π.
ca. 480
Chinese scholar Z
U
C
HONGZHI
(430–500) uses the
value 355/113 for π.
540 Appendix I