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Point, Lines, Planes, Angles
History of Early Geometry
Geometry
The word "geometry "
comes from two Greek words
geo and metron meaning "earth measuring."
Geometry was extremely important to ancient societies and
was used for surveying, astronomy, navigation, and building.
Geometry, as we know it is actually known as Euclidean
geometry which was written well over 2000 years ago in
Ancient Greece by Euclid,
Pythagoras, Thales,
Plato and Aristotle just to mention a few. The most
fascinating and accurate geometry text was written by Euclid,
and was called Elements. Euclid's text has been used for
over 2000 years!
History
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Thales of Miletus (624-547 BC)
Pythagoras of Samos (569-475 BC)
Hippocrates of Chios (470-410 BC)
Plato (427-347 BC)
Euclid of Alexandria (325-265 BC)
Archimedes of Syracuse (287-212 BC)
Where These People Lived
To understand the history, you need to know
the locations of the places being discussed.
Geography and geometry have a lot in common.
Let’s look at that section of the world.
Mediterranean
Thales
Thales of Miletus (624-547 BC)
was one of the Seven pre-Socratic
Sages, and brought the science of
geometry from Egypt to Greece. He is
credited with the experimental
discovery of five facts of elementary
geometry (including that an angle in a
semicircle is a right angle), but some
historians dispute this and give the
credit to Pythagoras.
Miletas
Black
Sea
Situated at the mouth of the Meander in the south of the province of
Ionia in Western Anatolia, the ancient city of Miletus was the oldest
and the most powerful of the twelve Ionian cities in Asia Minor. It also
founded over ten colonies on the shores of the Marmara and the
Black Sea, while its commercial activities extended as far as Egypt.
Its schools made a very great contribution to the intellectual and
scholarly development of the Mediterranean world and one cannot
talk of Miletus without mention of the great contributions to geometry
and science made by Thales, one of the greatest scholars produced
by the city.
Thales of Miletus
"The skillful man is superior to the strong man."
"Don't come to a conclusion before listening to both sides.“
"A small spark is enough to burn down a whole forest."
Pythagoras
Pythagoras of Samos (569-475 BC)
is regarded as the first pure mathematician
to logically deduce geometric facts from
basic principles. He is credited with proving
many theorems such as the angles of a
triangle summing to 180 deg, and the
infamous "Pythagorean Theorem" for a rightangled triangle (which had been known
experimentally in Egypt for over 1000 years).
The Pythagorean school is considered as the
(first documented) source of logic and
deductive thought, and may be regarded as
the birthplace of reason itself. As
philosophers, they speculated about the
structure and nature of the universe: matter,
music, numbers, and geometry.
Note that Samos is much closer to Turkey than Greece.
Samos
Greek Island
Fishing and resort island.
Hippocrates
Hippocrates of Chios (470-410 BC)
wrote the first "Elements of Geometry" which
Euclid may have used as a model for his own
Books I and II more than a hundred years later.
In this first "Elements", Hippocrates included
geometric solutions to quadratic equations and
early methods of integration. He studied the
classic problem of squaring the circle showing
how to square a "line". He worked on duplicating
the cube which he showed equivalent to
constructing two mean proportionals between a
number and its double. Hippocrates was also the
first to show that the ratio of the areas of two
circles was equal to the ratio of the squares of
their radii.
Chios
Note that Chios
is closer
to Turkey
than Greece.
Chios
Plato
Plato (427-347 BC)
founded "The Academy" in 387 BC which
flourished until 529 AD. He developed a theory
of Forms, in his book "Phaedo", which
considers mathematical objects as perfect
forms (such as a line having length but no
breadth). He emphasized the idea of 'proof'
and insisted on accurate definitions and clear
hypotheses, paving the way to Euclid, but he
made no major mathematical discoveries
himself. The state of mathematical knowledge
in Plato's time is reconstructed in the
scholarly book: The Mathematics of Plato's
Academy .
Athens
The Parthanon
Euclid
Euclid of Alexandria (325-265 BC)
is best known for his 13 Book
treatise "The Elements" (~300 BC),
collecting the theorems of
Pythagoras, Hippocrates,
Theaetetus, Eudoxus and other
predecessors into a logically
connected whole. A good modern
translation of this historic work is
The Thirteen Books of Euclid's
Elements by Thomas Heath.
Euclid Quote
When Pharaoh Ptolemy the ruler of Egypt said he wanted to learn
geometry, Euclid explained that the Pharaoh would have to study
long hours and memorize the contents of a fat book. Ptolemy
complained that it would be unseemly and demanded a short cut.
Euclid replied,
“There is no royal road to geometry.”
There wasn’t a shortcut to the learning process then
and there still isn’t one.
Homework needs to be done EVERY day.
Euclid Quote
A youth who had begun to read geometry
with Euclid, when he had learnt the first
proposition, he inquired, "What do I get by
learning these things?" So Euclid called a
slave and said "Give him three pence, since
he must make a gain out of what he learns."
“The laws of nature are but the
mathematical thoughts of God.”
Archimedes
Archimedes of Syracuse (287-212 BC)
is regarded as the greatest of Greek mathematicians,
and was also an inventor of many mechanical devices
(including the screw, the pulley, and the lever). He
perfected integration using Eudoxus' method of
exhaustion, and found the areas and volumes of many
objects. A famous result of his is that the volume of a
sphere is two-thirds the volume of its circumscribed
cylinder, a picture of which was inscribed on his tomb.
He gave accurate approximations to pi and square
roots. BC.
The father of mechanics.
Archimedes
In his treatise "On Plane Equilibriums", he set out
the fundamental principles of mechanics, using the
methods of geometry, and proved many
fundamental theorems concerning the center of
gravity of plane figures. He discovered the 13 semiregular (or "Archimedian") polyhedra whose faces
are all regular polygons. Translations of his
surviving manuscripts are now available as The
Works of Archimedes. A good biography of his life
and discoveries is also available in the book
Archimedes: What Did He Do Beside Cry Eureka?.
He was killed in Carthage by a Roman soldier 212
BC.
Syracuse: Greece?
Greek Colony of Syracuse
What did one acorn say
to another acorn?
Gee I’m a tree.
Groan?
Summary
1. Note that Geometry was not invented by the Greeks.
Euclid, the father of Geometry, did not discover it all.
Much work was done prior to him by Egyptians.
2. The three top ancient geometers were
Pythagoras,
Euclid,
and Archimedes
3. Geometry means measure the earth.
C’est fini.