Projective Versus Affine Spaces
In an affine space such as the Euclidean plane a similar statement is true, but only if one lists various exceptions involving parallel lines. Desargues' theorem is therefore one of the most basic of simple and intuitive geometric theorems whose natural home is in projective rather than affine space.
Read more about this topic: Desargues' Theorem
Famous quotes containing the word spaces:
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)