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Term/Theorem
Term/Theorem

Spring 2015 Axiomatic Geometry Lecture Notes
Spring 2015 Axiomatic Geometry Lecture Notes

Ans. - oxford high school
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... Inductive Reasoning: Reasoning by which a conclusion is based on several past observations. Deductive Reasoning: Proving statements by reasoning from accepted postulates, definitions, theorems, and given information. Counterexample: An example to prove an if-then statement false. Supplementary Angle ...
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... one-one correspondence between the points of R2 (except (0, 0)) and the lines that omit the origin; this is called a point-line duality. In Euclidean geometry we do not have a complete duality between all the points and all the lines that complete duality, which is very useful, is available in proj ...
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... Now, We will look at the axiom system structure itself and its properties. It is important to point out that, in an axiom system, it does not matter what the terms represent. The only thing that matters is how the terms are related to each other. In the last example, we can re-label the two terms st ...
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Duality (projective geometry)

In geometry a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language (§ Principle of Duality) and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a duality. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry.
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