History of Geometry
||c. 2000 - 500 B.C.
Ancient Egyptians demonstrated a practical knowledge of geometry through
surveying and construction projects.
||c. 2000 - 500 B.C.
Ancient clay tablets reveal that the Babylonians knew the Pythagorean
relationships. One clay tablet reads
4 is the length and 5 the diagonal. What is the breadth? Its size is
not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and
there remains 9. What times what shall I take in order to get 9? 3 times
3 is 9. 3 is the breadth.
||c. 750-250 B.C.
Ancient Greeks practiced centuries of experimental geometry like Egypt and
Babylonia had, and they absorbed the experimental geometry of both of
those cultures. Then they created the first formal mathematics of any kind
by organizing geometry with rules of logic. Euclid's (400BC) important
geometry book The Elements formed the basis for most of the
geometry studied in schools ever since.
|The Fifth Postulate
||c. 400 B.C. - 1800 A. D.
There are two main types of mathematical (including geometric) rules : postulates
(also called axioms), and theorems. Postulates are basic
assumptions - rules that seem to be obvious and are therefore accepted
without proof. Theorems are rules that must be proved.
Euclid gave five postulates. The fifth postulate reads: Given a line
and a point not on the line, it is possible to draw exactly one line
through the given point parallel to the line.
Euclid was not satisfied with accepting the fifth postulate (also known
as the parallel postulate) without proof. Many mathematicians throughout
the next centuries unsuccessfully
attempted to prove Euclid's Fifth.
|The Search for pi
||??? B.C. - present
It seems to have been known from most ancient of times that the ratio of
the circumference and diameter of a circle is a constant, but what is that
||c. 1600 A.D.
Descartes made one of the greatest advances in geometry by connecting
algebra and geometry. A myth is that he was watching a fly on the ceiling
when he conceived of locating points on a plane with a pair of numbers.
Maybe this has something to do with the fact that he stayed in bed
everyday until 11:00 A.M. Fermat also discovered coordinate geometry, but
it's Descartes' version that we use today.
||c. early 1800's
Since mathematicians couldn't prove the 5th postulate, they devised new
geometries with "strange" notions of parallelism. (A geometry
with no parallel lines?) Bolyai and Lobachevsky are credited with devising
the first non-euclidean geometries.
||c. late 1800's-1900's|
Differential geometry combines geometry with the techniques of calculus to
provide a method for studying geometry on curved surfaces. Gauss and
Riemann (his student) laid the foundation of this field. Einstein credits
Gauss with formulating the mathematical fundamentals of the theory of
||c. late 1800's-1900's
Fractals are geometric figures that model many natural structures like
ferns or clouds. The invention of computers has greatly aided the study of
fractals since many calculations are required. Mandlebrot is one of the
researchers of fractal geometry.