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A Transformation Approach to Tenth Grade Geometry, The Mathematics Teacher, Vol. 65, No. 1 (January 1972), pp. 21-30. Zalman P. Usiskin. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, Journal for Research in Mathematics Education, Vol. 3, No. 4 (Nov., 1972), pp. 249-259.
Heinrich Guggenheimer (1977) Differential Geometry, Dover, New York, ISBN 0-486-63433-7. Covers the work of Lie, Klein and Cartan. On p. 139 Guggenheimer sums up the field by noting, "A Klein geometry is the theory of geometric invariants of a transitive transformation group (Erlangen program, 1872)".
Download as PDF; Printable version; In other projects ... Affine transformation (Euclidean geometry) ... Legendre transformation; Möbius transformation; Perspective ...
In 3D plane-based GA, points 3-reflections. Algebraically this means they are grade-3 – but their geometric interpretation is very different from the usual geometric interpretation of a "trivector" as an "oriented volume element". The algebra of all distance-preserving transformations in 3D is called the Euclidean Group, ().
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation.
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative to a fixed frame of reference or coordinate system (alibi meaning "being somewhere else at the same time"); and passive or alias transformations which leave points fixed but change the ...
Since {,,} is mapped to {,,}, and Möbius transformations permute the generalised circles in the complex plane, maps the real line to the unit circle. Furthermore, since f {\displaystyle f} is a homeomorphism and i {\displaystyle i} is taken to 0 by f {\displaystyle f} , the upper half-plane is mapped to the unit disk .
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