Search results
Results From The WOW.Com Content Network
Naikan (Japanese: 内観, lit. ' introspection ') is a structured method of self-reflection developed by Yoshimoto Ishin (1916–1988) in the 1940s. [1] The practice is based around asking oneself three questions about a person in one's life: [2]
Call the images of p 2 and p 3 under this reflection p 2 ′ and p 3 ′. If q 2 is distinct from p 2 ′, bisect the angle at q 1 with a new mirror. With p 1 and p 2 now in place, p 3 is at p 3 ″; and if it is not in place, a final mirror through q 1 and q 2 will flip it to q 3. Thus at most three reflections suffice to reproduce any plane ...
(A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.
The translations here arise from the glide reflections, so this group is generated by a glide reflection and either a rotation or a vertical reflection. p11m [∞ +,2] C ∞h Z ∞ ×Dih 1 ∞* jump (THG) Translations, Horizontal reflections, Glide reflections: This group is generated by a translation and the reflection in the horizontal axis.
E.g., in the third case: translation by an amount b changes x into x + b, reflection with respect to 0 gives−x − b, and a translation a gives a − b − x. This group is called the generalized dihedral group of Z, Dih(Z), and also D ∞. It is a semidirect product of Z and C 2. It has a normal subgroup of index 2 isomorphic to Z: the ...
The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...
This larger group is the group of all motions of a rigid body: each of these is a combination of a rotation about an arbitrary axis and a translation, or put differently, a combination of an element of SO(3) and an arbitrary translation.
Any combination of reflections, translations, and rotations is called an isometry. Any combination of reflections, dilations, translations, and rotations is a similarity . All of these are conformal maps , and in fact, where the space has three or more dimensions, the mappings generated by inversion are the only conformal mappings.