- Oct 14, 2009
- 150
- 72
Let me explain. Whenever I look up pretty much anything to do with mathematics, it goes straight to the details, skipping over the general overview which anyone skimming would almost always prefer.
Here's an example, Euclidean space:
Now I'm generally a high-flier and at home with this stuff, but if I want to understand it without spending 5 minutes of my life finding the simple definition, I sure as hell can't be on wikipedia.
Has anyone else noticed that around here?
Here's an example, Euclidean space:
wikipedia said:In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term “Euclidean” is used to distinguish these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity.
In classical Greek geometry, the Euclidean plane and Euclidean three-dimensional space were defined using certain postulates, and the other properties of these spaces were deduced as theorems. In modern mathematics, it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry. This approach brings the tools of algebra and calculus to bear on questions of geometry, and has the advantage that it generalizes easily to Euclidean spaces of more than three dimensions.
From the modern viewpoint, there is essentially only one Euclidean space of each dimension. In dimension one this is the real line; in dimension two it is the Cartesian plane; and in higher dimensions it is the real coordinate space with three or more real number coordinates. Thus a point in Euclidean space is a tuple of real numbers, and distances are defined using the Euclidean distance formula. Mathematicians often denote the n-dimensional Euclidean space by , or sometimes if they wish to emphasize its Euclidean nature.
Now I'm generally a high-flier and at home with this stuff, but if I want to understand it without spending 5 minutes of my life finding the simple definition, I sure as hell can't be on wikipedia.
Has anyone else noticed that around here?