Functions and mappings | Linear operators | Transformation (function) | Euclidean symmetries
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis would look like q. Its image by reflection in a horizontal axis would look like b. A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state. The term reflection is sometimes used for a larger class of mappings from a Euclidean space to itself, namely the non-identity isometries that are involutions. Such isometries have a set of fixed points (the "mirror") that is an affine subspace, but is possibly smaller than a hyperplane. For instance a reflection through a point is an involutive isometry with just one fixed point; the image of the letter p under itwould look like a d. This operation is also known as a central inversion , and exhibits Euclidean space as a symmetric space. In a Euclidean vector space, the reflection in the point situated at the origin is the same as vector negation. Other examples include reflections in a line in three-dimensional space. Typically, however, unqualified use of the term "reflection" means reflection in a hyperplane. Some mathematicians use "flip" as a synonym for "reflection". (Wikipedia).
Light and Optics 1_3 Introduction to Reflection
Reflection from plane and spherical mirrors.
From playlist Physics - Light and Optics
Light and Optics 1_2 Introduction to Reflection
Reflection form plane and spherical mirrors
From playlist Physics - Light and Optics
Light and Optics 1_6 Introduction to Reflection
Reflection. Solved problems.
From playlist Physics - Light and Optics
Light and Optics 1_5 Introduction to Reflection
Reflections. Solved Problems.
From playlist Physics - Light and Optics
First video in a series on reflection and refraction.
From playlist Physics - Reflection and Refraction
Light and Optics 1_1 Introduction to Reflection
Reflection and refraction
From playlist Physics - Light and Optics
Light and Optics 3_1 More on Reflection and Refraction
A more in depth look at reflection and refraction.
From playlist Physics - Light and Optics
Physics 11.1.1b - The Law of Reflection
The Law of Reflection
From playlist Physics - Reflection and Refraction
Light and Optics 1_4 Introduction to Reflection
Examples of plane and spherical mirror problems.
From playlist Physics - Light and Optics
Journée de la Revue d’histoire des mathématiques - Catherine Radtka - 01/12/17
Journée de la Revue d’histoire des mathématiques (séance préparée par la rédaction de la RHM) Catherine Radtka (UMR FEMTO-ST/RECITS, CNRS & Université de technologie de Belfort-Montbéliard), « De l'Université au primaire et retour : quelles continuité et unité disciplinaires dégager au
From playlist Séminaire d'Histoire des Mathématiques
Reflections in hyperbolic geometry | Universal Hyperbolic Geometry 14 | NJ Wildberger
Symmetries are crucial in studying geometry. In Euclidean geometry we have translations, rotations, reflections, dilations and also projections and perspectivities. This lecture introduces reflections into universal hyperbolic geometry. First we discuss the two different kinds of reflectio
From playlist Universal Hyperbolic Geometry
Reflections and projective linear algebra | Universal Hyperbolic Geometry 15 | NJ Wildberger
Reflections are the fundamental symmetries in hyperbolic geometry. The reflection in a point interchanges any two null points on any line through the point. Using the projective parametrization of the circle, we associate to the reflecting point a 2x2 projective matrix. So we need to devel
From playlist Universal Hyperbolic Geometry
Midpoints and bisectors | Universal Hyperbolic Geometry 16 | NJ Wildberger
Midpoints of sides may be defined in terms of reflections in points in hyperbolic geometry. Reflections are defined by 2x2 trace zero matrices associated to points. The case of a reflection in a null point is somewhat special. The crucial property of reflection is that it preserves perpend
From playlist Universal Hyperbolic Geometry
Rubik, Escher, Banks - Brian Conrad (Stanford University)
The idea of geometric symmetry in architecture goes back to ancient times, but there is a rich mathematical theory of symmetry with many applications in the modern world. The mathematics of symmetry provides answers to natural questions that arise in topics as diverse as Rubik's Cube, the
From playlist Mathematics Research Center
Applications of 3x3 matrices | Wild Linear Algebra A 11 | NJ Wildberger
This is the 11th lecture in this course on Linear Algebra by N J Wildberger. Here we talk about 3x3 matrices and their applications to linear transformations of three dimensional space. This includes dilations, reflections, rotations with plenty of examples. CONTENT SUMMARY: pg 1: @00:08
From playlist WildLinAlg: A geometric course in Linear Algebra
"Jeux de lumières" par Etienne Ghys au CIRM en YouTube-Live
Un exposé d'Etienne Ghys dans le cadre de la cérémonie des 40 ans du CIRM. Diffusion en direct le jeudi 14 octobre 2021 à 14 heures. Étienne Ghys est un mathématicien français, secrétaire perpétuel (première division) de l'Académie des sciences. Il est directeur de recherche au CNRS, affe
From playlist OUTREACH - GRAND PUBLIC
This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans
From playlist Math talks
Chemistry 107. Inorganic Chemistry. Lecture 01
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 01. Inorganic Chemistry -- Course Introduction & Symmetry of Nature View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://
From playlist Chem 107: Week 1
Translations, rotations and reflections (III) | Arithmetic and Geometry Math Foundations 37
We introduce reflections acting on vectors, not points, in a similar way to rotations in the last video. Now the product of two reflections is a rotation. This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics. Vi
From playlist Math Foundations
Physics 51 - Optics: Reflections (1 of 2) Introduction
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the concepts of light reflections and show you how to find the angle between the inbound and exit ray.
From playlist PHYSICS - OPTICS