youth who had begun to read geometry with Euclid, when he had learnt the first
inquired, "What do I get by learning these things?" So Euclid called a slave and said "Give him
threepence, since he must make a gain out of what he learns."
Euclid, quoted in Stobaeus, Extracts
As to writing another book on geometry, the middle ages would have as soon
thought of composing
another New Testament.
Augustus De Morgan
Geometry (which is the only science that it hath pleased God to bestow on
Thomas Hobbes, Leviathan 1651
Geometry is the science of correct reasoning on incorrect figures.
In order to translate a sentence from English into French two things are
necessary. First, we must
understand thoroughly the English sentence. Second, we must be familiar with the forms of
expression peculiar to the French language. The situation is very similar when we attempt to express
in mathematical symbols a condition proposed in words. First, we must understand thoroughly the
condition. Second, we must be familiar with the forms of mathematical expression.
Mathematics is the art of giving the same name to different things.
[As opposed to the quotation: Poetry is the art of giving different names to the same thing].
What then are we to think of the question: Is Euclidean geometry true? It
has no meaning. We might as well ask if the metric system is true and if the
old weights and measures are false; if Cartesian coordinates are true and polar
coordinates are false. One geometry cannot be more true
than another; it can only be more convenient.
Henri Poincaré, Quoted in M J Greenberg, Euclidean and non-Euclidean geometries: Development and history (San Fransisco, 1980).
Geometria una et aeterna est in mente Dei
refulgens: cuius consortium hominibus tributum
inter causas est, cur homo sit imago Dei.
Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of
the reasons that Man is the image of God.
Johannes Kepler, Conversation with the Sidereal Messenger [an open letter to Galileo Galilei]: Dissertatio cum Nuncio Sidereo (Prague, 1610) KGW 4 308, lines 9 - 10.
Euclid taught me that without assumptions there is no proof. Therefore, in
any argument, examine the assumptions.
Eric Temple Bell, Quoted in H. Eves Return to Mathematical Circles., Boston: Prindle, Weber and Schmidt, 1988.
Guided only by their feeling for symmetry, simplicity, and generality, and
an indefinable sense of the
fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics
rather than by any prospect of ultimate usefulness.
Eric Temple Bell
"Obvious" is the most dangerous word in mathematics.
Eric Temple Bell
Pure mathematics is on the whole distinctly more useful than applied For what is useful above all is
technique, and mathematical technique is taught mainly through pure mathematics.
G H Hardy
At the age of eleven, I began Euclid, with my brother as my tutor. This was
one of the great events
of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world.
From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of
Bertrand Russell, The Autobiography of Bertrand Russell .
Geometry is the noblest branch of physics.
William F Osgood, Quoted in D MacHale, Comic Sections (Dublin 1993)
Euclid, Biography of Euclid (325BC-265BC)
Euclid's Elements, This dynamically illustrated edition of Euclid's Elements includes 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry.
Byrne's edition of Euclid, Oliver Byrne's edition of Euclid An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne.
NonEuclid is a Java Software Simulation offering Ruler and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry (a geometry of Einstein's General Relativity Theory and Curved Hyperspace) for use in High School and Undergraduate Education.
The Geometry Junkyard,
David Eppstein, UC Irvine. A mix of recreational geometry and
The Geometry Forum, Swarthmore
College, concerns itself with K-12 geometry education, but
also maintains a geometry research mailing list with archives on their web site.
Geometry in Action, This page collects various areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications.
Geometry Forum -
Shapiro, Geometry Through Art What Children Can Learn about Art and
Geometry If you would like to view the sketches included in this unit, you will
need a copy of The
Non-Euclidean geometry In about 300 BC Euclid wrote The Elements, a book which was to become one of the most famous books ever written. Euclid stated five postulates on which he based all his theorems