Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triagular prism is a right triangular prism with equilateral bases, and square sides.

Equivalently, it is a pentahedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes). These three faces are parallelograms. All cross-sections parallel to the base faces are the same triangle.

As a semiregular (or uniform) polyhedron

A right triangular prism is semiregular or, more generally, a uniform polyhedron if the base faces are equilateral triangles, and the other three faces are squares. It can be seen as a truncated trigonal hosohedron, represented by Schläfli symbol t{2,3}. Alternately it can be seen as the Cartesian product of a triangle and a line segment, and represented by the product {3}x{}. The dual of a triangular prism is a triangular bipyramid.

Trip (Cause and Effect album)

Trip is the second album from the synthpop act Cause and Effect. It is dedicated to the memory of Sean Rowley. The album includes the song "It's Over Now," which climbed to the #7 spot on Billboard's modern rock charts. It was released in 1994 under the BMG label.

Track listing

Personnel

References

Trip (Hedley song)

"Trip" is a pop punk song recorded by Canadian band Hedley and appears on their debut album Hedley (2005). The single topped the Canadian MuchMusic Countdown and reached number eleven on the Canadian Singles Chart. It sold close to 3,000 copies. Trip appears on the US version of Famous Last Words, which is called Never Too Late.

Charts

External links

Dimension (song)

"Dimension" is a song by Australian hard rock band Wolfmother, featured on their 2005 debut studio album Wolfmother. Written by band members Andrew Stockdale, Chris Ross and Myles Heskett, it was released as the second single from the album in Europe (and the third single overall) on 17 April 2006, charting at number 49 on the UK Singles Chart.

Music video

Directed by The Malloys, the music video for "Dimension" was first aired in the week of 13 February 2006. Prior to this, the video was featured on the 2006 extended play (EP) Dimensions.

Critical reception

In a review of Wolfmother for Blender, writer Jonah Weiner identified "Dimension" as an example of the band "at [their] hardest", describing it as an "acid anthem".NME reviewer James Jam described the song as "a throb of gonzo metal not unlike Black Sabbath playing Motown".

Track listing

All songs written and composed by Andrew Stockdale, Chris Ross, Myles Heskett. 

References

Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their fundamental dimensions (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed. Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.

The concept of physical dimension was introduced by Joseph Fourier in 1822. Physical quantities that are commensurable have the same dimension; if they have different dimensions, they are incommensurable. For example, it is meaningless to ask whether a kilogram is less, the same, or more than an hour.

Any physically meaningful equation (and likewise any inequality and inequation) will have the same dimensions on the left and right sides, a property known as "dimensional homogeneity". Checking this is a common application of dimensional analysis. Dimensional analysis is also routinely used as a check on the plausibility of derived equations and computations. It is generally used to categorize types of physical quantities and units based on their relationship to or dependence on other units.

Dimension (graph theory)

In mathematics, and particularly in graph theory, the dimension of a graph is the least integer such that there exists a "classical representation" of the graph in the Euclidean space of dimension with all the edges having unit length.

In a classical representation, the vertices must be distinct points, but the edges may cross one another.

The dimension of a graph is written: .

For example, the Petersen graph can be drawn with unit edges in , but not in : its dimension is therefore 2 (see the figure to the right).

This concept was introduced in 1965 by Paul Erdős, Frank Harary and William Tutte. It generalises the concept of unit distance graph to more than 2 dimensions.

Examples

Complete graph

In the worst case, every pair of vertices is connected, giving a complete graph.

To immerse the complete graph with all the edges having unit length, we need the Euclidean space of dimension . For example, it takes two dimensions to immerse (an equilateral triangle), and three to immerse (a regular tetrahedron) as shown to the right.