(33) So far we have been using three-mensional perceived space and Euclidean geometry
While all students have generally been exposed to Euclidean geometry
, most do not know much about non-Euclidean geometries and are very intrigued, if at times baffled, by this different perspective.
Moreover, the process of solution employing different methods and techniques involves the application of rules of the subjects of Euclidean geometry
and other fields , their integration and reinforcement both in the sense of their specific required skills, and, in some cases also skills from other mathematical fields such as algebraic skills, as a byproduct.
If space is curved then Euclidean geometry
, which is one of many axiomatic systems, does not apply.
in Euclidean geometry
. We observe that the previous equality is a equivalent form to the Van Aubel's theorem of euclidian geometry.
Let's consider Hilbert's 21 axioms of Euclidean geometry
. If we Smarandachely deny one, two, three, and so on, up to 21 axioms respectively, then one gets:
Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry
, Washington, DC: Math.
Guys, study your Euclidean geometry
: The intersection of a line and a plane has a simple angle of incidence.
Before hyperbolic geometry was discovered, it was thought to be completely obvious that Euclidean geometry
correctly described physical space, and attempts were even made, by Kant and others, to show that this was necessarily true.
Although Einstein didn't excel in high school in Munich, he had already begun educating himself on Euclidean geometry
, deductive reasoning and calculus using textbooks borrowed from a family friend.
Alys's artistic affinity with the Situationist International and neo-dada movements like Fluxus manifests itself in his efforts to conjure an experiential map for the city through arbitrary social encounters, which transcend the confining Euclidean geometry
of modern urban planning.
In mathematics, Euclidean geometry
used to be taught in something close to its original presentation two thousand years ago as a rational progression of ideas.