**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Symmetry in Space: Rotororeflections

Description

This lecture explores the concept of rotororeflections, which are transformations resulting from the composition of three plane reflections in space. It covers the normalization of the product of three reflections into a rotororeflection, the determination of four equivalent planes in a rotororeflection, and the creation of mirrored pieces. The lecture also delves into practical applications in computer-aided design, revolution symmetries, and equivalent displacements. The instructor demonstrates the commutation of orthogonal plans and the fundamental theorem of isometries in space. The lecture concludes with an overview of the 10 isometries in space and an artistic interlude on the Contrapposto posture in art.

Login to watch the video

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Instructor

In course

Related concepts (381)

MATH-124: Geometry for architects I

Ce cours entend exposer les fondements de la géométrie à un triple titre :
1/ de technique mathématique essentielle au processus de conception du projet,
2/ d'objet privilégié des logiciels de concept

In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. The main use for planes of rotation is in describing more complex rotations in four-dimensional space and higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra.

In telecommunications, packet switching is a method of grouping data into packets that are transmitted over a digital network. Packets are made of a header and a payload. Data in the header is used by networking hardware to direct the packet to its destination, where the payload is extracted and used by an operating system, application software, or higher layer protocols. Packet switching is the primary basis for data communications in computer networks worldwide.

In geometry, a point reflection (also called a point inversion or central inversion) is an transformation of affine space in which every point is reflected across a specific fixed point. A point reflection is an involution: applying it twice is the identity transformation. It is equivalent to a homothetic transformation with scale factor −1. The point of inversion is also called homothetic center. An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Multiprotocol Label Switching (MPLS) is a routing technique in telecommunications networks that directs data from one node to the next based on labels rather than network addresses. Whereas network addresses identify endpoints the labels identify established paths between endpoints. MPLS can encapsulate packets of various network protocols, hence the multiprotocol component of the name. MPLS supports a range of access technologies, including T1/E1, ATM, Frame Relay, and DSL. In an MPLS network, labels are assigned to data packets.

Related lectures (1,000)

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Symmetry in Modern Geometry

Explores modern symmetry in geometry, focusing on the Klein bottle and different types of transformations.

Symmetry in Modern Geometry

Explores the modern definition and practical applications of symmetry in geometry.

Symmetry in Modern Geometry

Explores symmetry theorems, isometries classification, practical applications, friezes, and planar tessellations.