Triangle - Basic facts

Triangle - Basic facts: Encyclopedia II - Triangle - Basic facts

Elementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE. A triangle is a polygon and a 2-simplex (see polytope). All triangles are two-dimensional. Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the si ...

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Triangle - Non-planar triangles

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Triangle - Basic facts: Encyclopedia II - Triangle - Points, lines and circles associated with a triangle

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

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Bermuda Triangle - History of the Bermuda Triangle

Bermuda Triangle - Scientific explanations

Bermuda Triangle - Famous incidents

Bermuda Triangle - Flight 19

Triangle - Basic facts: Encyclopedia - Trigonometric function

In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to comp ...

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Trigonometric function - Relationship to exponential function

Trigonometric function - Definitions via differential equations

Trigonometric function - The significance of radians

Triangle - Basic facts: Encyclopedia - Inversive geometry

In mathematics, inversive geometry is the geometry of circles and the set of transformations that map all circles into circles, where by a circle one may also mean a line (a circle with infinite radius). Inversive geometry - Circle inversion. Inversive geometry - Inverse of a point. In the plane, the inverse of a point P in respect to a circle of center O and radius R is a point P' such that P and P' are on the same ray goi ...

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Inversive geometry - Circle inversion

Triangle - Basic facts: Encyclopedia - Collision detection

In physical simulations, video games and computational geometry, collision detection includes algorithms from checking for collision, i.e. intersection, of two given solids, to calculating trajectories, impact times and impact points in a physical simulation. Collision detection - Overview. In physical simulation, we wish to conduct experiments, such as playing billiards. The physics of bouncing billiard balls are well understood, under the umbrella of rigid body motion and elastic collisions. An initial de ...

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Triangle - Basic facts: Encyclopedia - Wassily Kandinsky

Wassily Kandinsky (Russian: Василий Кандинский, first name spelled as [vassi:li]) (December 4, 1866 (O.S., December 16, 1866 N.S.) – December 13, 1944) was a Russian-born French painter and art theorist. One of the most important 20th-century artists, alongside Picasso and Matisse, he is credited with painting the first abstract works in the history of modern art. Kandinsky was born in Moscow but spent his childhood in Odessa. He enrolled at the University of Moscow and chose law and economics. Although quite successful in his profession, he started painting studies ...

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Wassily Kandinsky - Artistic periods

Wassily Kandinsky - Theoretical writings on Art

Triangle - Basic facts: Encyclopedia - Bicycle frame

A bicycle frame is the main component of a bicycle, onto which wheels and other components are fitted. The modern and most common frame design for an upright bicycle is based on the safety bicycle, and is made of two triangles, a main triangle and a paired rear triangle. This is known as the diamond frame. The main triangle consists of the head tube, top tube, down tube and seat tube. The rear triangle consists of the seat tube, and paired chain stays and seat stays. The head tube contains the headset, the interface with the fo ...

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Bicycle frame - Frame tubes

Bicycle frame - Frame geometry

Bicycle frame - Frame materials

Triangle - Basic facts: Encyclopedia - Star of David

The Star of David (Hebrew Magen David or Mogen Dovid מגן דוד, Arabic Najmat Dawuud نجمة داوود). It is also known as Solomon's Seal, or Seal of Solomon (Ashkenazi Hebrew, Shield of David, Arabic Khatam Sulayman خاتم سليمان) is a generally recognized symbol of Judaism and Jewish identity, although it has been used also in Islam as well as the Eastern Religions. Geometrically it is a hexagram. It i ...

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Star of David - Origin

Triangle - Basic facts: Encyclopedia - Blaise Pascal

Blaise Pascal (June 19, 1623–August 19, 1662) was a French mathematician, physicist, and religious philosopher. Pascal was a child prodigy, who was educated by his father. Pascal's earliest work was in the natural and applied sciences, where he made important contributions to the construction of mechanical calculators and the study of fluids, and clarified the concepts of pressure and vacuum by expanding the work of Evangelista Torricelli. Pascal also w ...

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Blaise Pascal - Mature life religion philosophy and literature

Triangle - Basic facts: Encyclopedia - 3D computer graphics

The rewrite of this article is being devised at Talk:3D computer graphics/Temp. Please comment or help out as necessary. Thanks! 3D computer graphics are works of graphic art that were created with the aid of digital computers and specialized 3D software. In general, the term may also refer to the process of creating such graphics, or the field of study of 3D computer graphic techniques and its related technology. 3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the p ...

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3D computer graphics - Modeling

3D computer graphics - Process

Triangle - Basic facts: Encyclopedia - Axiom

In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. Not all epistemologists agree that any axioms, understood in that sense, exist. In mathematics, an axiom is not necessarily a self-evident truth but rather, a formal logical expression used in a deduction to yield further results. Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms. Axiom - Etymology. The word axiomIncluding:

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Triangle - Basic facts: Encyclopedia - Anti-aliasing

In digital signal processing, anti-aliasing is the technique of minimizing aliasing (jagged or blocky patterns) when representing a high-resolution signal at a lower resolution. In most cases, anti-aliasing means removing data at too high a frequency to represent. When sampling is performed without removing this part of the signal, it causes undesirable artifacts such as the black-and-white noise near the top of figure 1-a. In signal acquisition, this is often done using an analog anti-aliasing filter to remove the out-of-band component of the input signal pr ...

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Anti-aliasing - Mipmapping

Triangle - Basic facts: Encyclopedia - Consonance and dissonance

In music, a consonance (Latin consonare, "sounding together") is a harmony, chord, or interval considered stable, as opposed to a dissonance, which is considered unstable. The strictest definition of consonance may be only those sounds which are pleasant, while the most general definition includes any sounds which are used freely. Consonance and dissonance - Consonance. Consonance has been defined variously through: Frequency ratios: with ratios of lower simple numbers being more ...

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Consonance and dissonance - Consonance

Consonance and dissonance - Source

Consonance and dissonance - Dissonance

Triangle - Basic facts: Encyclopedia - Quantum

The word quantum, pl. "quanta", comes from the Latin "quantus", for "how much". In general, it refers to an "amount of something". But, the term is often used in the more specific sense which it has in physics, where a quantum refers to an indivisible, and perhaps elementary entity. For instance, a "light quantum", being a unit of light (that is, a photon). In combinations like "quantum mechanics", "quantum optics", etc., it di ...

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Quantum - Discovery of quantum theory

Quantum - Quantization in antiquity

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Triangle - Basic facts: Encyclopedia - Sound

Sound is vibration, as perceived by the sense of hearing. We usually hear vibrations that travel through air, but sound can also travel through gases, liquids and solids. It cannot travel through a vacuum (such as exists in outer space). When the vibrations reach our ears, they are converted into nerve impulses that are sent to our brains, allowing us to perceive the sound. In more technical language, sound "is an alternation in pressure, particle displacement, or particle velocity propagated in an elastic material" (Olson 1957 ...

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Sound - Attributes of sound

Sound - Sound measurement

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