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Ceramic Tiles in Marrakech, forming edge-to-edge, regular and other tessellations A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semi-regular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. History[edit] A temple mosaic from the ancient Sumerian city of Uruk IV (3400–3100 BC) showing a tessellation pattern in the tile colours. Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles.[1] Etymology[edit] Overview[edit] Many other types of tessellation are possible under different constraints. Other methods also exist for describing polygonal tilings. [edit]

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Coxeter–Dynkin diagram Coxeter–Dynkin diagrams for the fundamental finite Coxeter groups Coxeter–Dynkin diagrams for the fundamental affine Coxeter groups Each diagram represents a Coxeter group, and Coxeter groups are classified by their associated diagrams. Dynkin diagrams are closely related objects, which differ from Coxeter diagrams in two respects: firstly, branches labeled "4" or greater are directed, while Coxeter diagrams are undirected; secondly, Dynkin diagrams must satisfy an additional (crystallographic) restriction, namely that the only allowed branch labels are 2, 3, 4, and 6. See Dynkin diagrams for details.

Hassell and Draisci Studio create sleeperie to encourage naps London Festival of Architecture 2015: visitors to this London "sleeperie" can take a 10-minute nap in a colourful sling within a dimly-lit room, where soothing music is played and all technology is banned (+ slideshow). London showroom Sto Werkstatt invited architecture offices Hassell and Draisci Studio to create an interactive exhibition exploring types of architectural spaces that can be used for short-term physical and mental rest. Called Hypnos: The Architecture of Sleep, the installation has been dubbed "London's first sleeperie". It encourages visitors to switch off mobile phones, tablets and laptops, and enjoy a quick daytime nap. According to the architects, technology's invasion of the bedroom has disrupted many people's sleeping patterns and has prevented them from being able to fully relax. "On the other side, as designers we are being asked to respond to this shift in sleep patterns and working practices by designing sleeping pods in work places or airports," he added.

List of convex uniform tilings This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane , and their dual tilings. There are three regular, and eight semiregular, tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type of irregular face. Uniform tilings are listed by their vertex configuration , the sequence of faces that exist on each vertex. For example means one square and two octagons on a vertex.

Archrecord2 - Architectural Record - Mafoombey explores the acoustics of cardboard By Dianna Dilworth Martti Kalliala and Esa Ruskeepää were college roommates while attending the architecture school at Helsinki University of Technology. The two students began to experiment with cut corrugated cardboard when they entered the open-to-all Habitare design contest at the University of Art and Design in Helsinki in 2005. The competition asked for a small space for listening to and experiencing music within the set dimensions of 2.5 cubic meters. Thus was born Mafoombey, a space for music. File:Pythagorean proof (1).svg The original description page is/was here. All following user names refer to en.wikipedia. 2010-07-15 04:40 Phildonnia 744×1052× (28485 bytes) {{Information |Description = |Source = I (~~~) created this work entirely by myself. |Date = ~~~~~ |Author = ~~~ |other_versions = }}

Architectural acoustics Architectural acoustics (also known as room acoustics and building acoustics) is the science and engineering of achieving a good sound within a building and is a branch of acoustical engineering.[1] The first application of modern scientific methods to architectural acoustics was carried out by Wallace Sabine in the Fogg Museum lecture room who then applied his new found knowledge to the design of Symphony Hall, Boston.[2] Architectural acoustics can be about achieving good speech intelligibility in a theatre, restaurant or railway station, enhancing the quality of music in a concert hall or recording studio, or suppressing noise to make offices and homes more productive and pleasant places to work and live in.[3] Architectural acoustic design is usually done by acoustic consultants.[4] Building skin envelope[edit] This science analyzes noise transmission from building exterior envelope to interior and vice versa.

Algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique. In the 20th century, algebraic geometry has split into several subareas. Basic notions[edit]

Dezeen To mark the release of his debut album Human, which came out last week, techno producer Max Cooper has exclusively shared a binaural mix with us, which features the new album’s lead track Woven Ancestry. Binaural recordings create a 3D sound experience: music seems to come from multiple different directions, as if you were sitting in the room with the musicians. The effect only works if you’re listening with headphones, though. So put on a pair of cans, close your eyes, and immerse yourself in the music! The mix, which was recorded live and also features the tracks Meadows and Gravity Well, was created using 4DSOUND, a rig consisting of 48 speakers arranged in 16 columns, which allows producers to spatially design the sounds within tracks. You can watch a video of Cooper explaining the project here.

Riemannian geometry Elliptic geometry is also sometimes called "Riemannian geometry". Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area, and volume. From those some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugurational lecture Ueber die Hypothesen, welche der Geometrie zu Grunde liegen (On the Hypotheses which lie at the Bases of Geometry). It is a very broad and abstract generalization of the differential geometry of surfaces in R3.

EKKO installation by Thilo Frank Visitors to this installation in northern Denmark by German artist Thilo Frank are invited to walk through a contorted loop of timber while listening to the sounds of their voices and footsteps played back to them (+ slideshow). A circle of concrete paving creates a continuous walkway, while 200 wooden frames with incrementally different dimensions provide the twisted structure surrounding it. Microphones are hidden within the wooden beams and record the sounds made by everyone that steps inside. Riemannian manifold In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product on the tangent space at each point that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then is a smooth function.

The Hear Heres by Studio Weave The sounds of the countryside are amplified when you place your ear towards one of these four enormous trumpets built by architects Studio Weave (+ slideshow). Named The Hear Heres, the horns are dotted along a walk through the grounds of Kedleston Hall, a stately home in Derbyshire, England. One horn is pointed down towards the surface of a lake (above), while another angles up towards the sky (below). The third trumpet winds around the the trunk of a tree, so listeners can hear the movements of the branches (below). When describing the fourth and largest of the trumpets (below), Studio Weave's Maria Smith told Dezeen how "it's fun for two people to sing to each other from opposite ends." She explained how the sound is loud on one side, but "sounds distant" from the other.