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lecture 25
lecture 25

... are equal. (Here len(s1 ) refers to the length of s1 , and so on...) We then talked about Descartes, who invented a cunning technique for turning problems in geometry into problems in algebra: the Cartesian plane. Each point in the plane is labelled with a pair of (real) numbers—the x coordinate, an ...
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... right angle- is an angle that measures 90˚ acute angle – an angle that measures less than 90˚ obtuse angle – an angle that measures greater than 90˚ and less than 180˚ straight angle – an angle that measures 180˚ parallel lines – are lines in a plane that are always the same distance apart. intersec ...
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Geometry Chapter 1 Test ReView Name: Period: Topics to be

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Chapter 1 – Points, Lines, Planes, and Angles

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Non-Euclidean Geometry, spring term 2017 Homework 4. Due date

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Unit1 Vocabulary Review (ISG1.1-1.3)

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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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