When did geometry originate?
The field of geometry was probably developed by several cultures over millennia, but
only in crude, elementary forms. Some of the first to actually work with geometry
were the cultures of the Mesopotamian region around 3500 BCE(especially the Babylo-
nians). They were the earliest peoples to know about what is now called the
Pythagorean theorem (in fact, the Greek mathematician and philosopher Pythagoras
of Samos [c. 582–c. 507 BCE] may have actually learned about this theorem in his trav-
els to the east), and they possessed all the theorems of plane geometry that the Greeks
attributed to Thales. The Egyptians came next, using geometric methods mainly for
construction of huge monuments. This included the sundry pyramids and monu-
ments of the region, some of which still dot the landscape today—a tribute to their
builders who used geometric techniques.Were the Greeksinvolved in geometry?
The Greeks were known to have extensive knowledge of geometry, producing many
great geometers. With this and other contributions in mathematics, the Greeks pro-
foundly changed the approach and character of the entire mathematical field. It is
thought that Thales of Miletus (c. 625–c. 550 BCE; Ionian) first introduced geometry to
the Greeks. As a merchant traveler, he was exposed to the Babylonian concept of mea-
surement, from which practices sprang geometry. Thales used his geometric knowl-
edge to solve problems such as the height of the pyramids and the distance of ships
from the shoreline.Greek geometer Hippocrates of Chios (470–410 BCE) was one of the first to present
an axiomatic approach to geometry, as well as the first to work on the elements almost
a century before Euclid (see below). Hippocrates may have worked on geometry and
such problems as squaring the circle, but he lacked common sense and was duped by
many people.Zeno of Elea (c. 490–c. 425 BCE) raised questions about lines, points, and num-
bers—all part of geometry—with his many paradoxes (for more information about
Zeno and his paradoxes, see “Foundations of Mathematics”). Another important figure
is Eudoxus of Cnidus (408–355 BCE), who worked on geometric proportions and theo-
ries for determining areas and volumes.Others followed these geometers, including Archimedes (c. 287–212 BCE; Hel-
lenic), who worked on mechanics and took the first steps toward integral calculus.
Apollonius of Perga (262–190 BCE), or the “great geometer,” first named and presented
theories on conic sections in his book Conics,and he introduced the terms “parabola,”
“ellipse,” and “hyperbola.” There was also Pappus of Alexandria (290–350), who pre-
sented the basis for modern projective geometry (the geometry that deals with inci-
166 dences, or whether elements such as lines, planes, and points coincide or not).