Euclidean Geometry

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Euclidean Geometry

The Plane geometry learned in high school, based upon a few ideal, smooth, symmetric shapes.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.

Euclidean Geometry

A system of geometry that deals with objects on a plane. Its theory is based on five postulates, from which a number of theoretical proofs are derived.
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Importantly, the essay provides insight into Fisher's reading of Kant's notion of intuitive (transcendental) knowledge, and Fisher's awareness of the growing challenge to the role of Euclidian geometry within Kant's space of intuition by pseudo-spherical geometry.
By dividing a line into an infinite series of infinitely small points, paradoxes and logical contradictions arose that defied the desired rationality and order of Euclidian geometry. If the parts are infinitely small, then the sum of their lengths should be zero.
I was reading the "Pass/Fail" (October/November 2009), and I determined that Patrick Sweeney passed his Euclidian geometry (2D) class but failed his solids geometry (3D) class.
The axiomatic structure of the Euclidian geometry forms a coherent field of objects and relations of a theoretical nature; and thus it constitutes a favorable ground for the learning of the reasoning and justification.
However, we do not suggest that Euclidian geometry was invented or even pre-echoed at Thera.