Arc (projective geometry)

A (simple) arc in finite projective geometry is a set of points which satisfies, in an intuitive way, a feature of curved figures in continuous geometries. Loosely speaking, they are sets of points that are far from "line-like" in a plane or far from "plane-like" in a three-dimensional space. In this finite setting it is typical to include the number of points in the set in the name, so these simple arcs are called k-arcs. An important generalization of the k-arc concept, also referred to as arcs in the literature, are the (k, d)-arcs.

k-arcs in a projective plane

In a finite projective plane π (not necessarily Desarguesian) a set A of k (k ≥ 3) points such that no three points of A are collinear (on a line) is called a k - arc. If the plane π has order q then k ≤ q + 2, however the maximum value of k can only be achieved if q is even. In a plane of order q, a (q + 1)-arc is called an oval and, if q is even, a (q + 2)-arc is called a hyperoval.

Every conic in the Desarguesian projective plane PG(2,q), i.e., the set of zeros of an irreducible homogeneous quadratic equation, is an oval. A celebrated result of Beniamino Segre states that when q is odd, every (q + 1)-arc in PG(2,q) is a conic. This is one of the pioneering results in finite geometry.

Arc (geometry)

In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve. A common example in the plane (a two-dimensional manifold), is a segment of a circle called a circular arc. In space, if the arc is part of a great circle (or great ellipse), it is called a great arc.

Every pair of distinct points on a circle determines two arcs. If the two points are not directly opposite each other, one of these arcs, the minor arc, will subtend an angle at the centre of the circle that is less than π radians (180 degrees), and the other arc, the major arc, will subtend an angle greater than π radians.

Circular arcs

Length of an arc of a circle

The length (more precisely, arc length), L, of an arc of a circle with radius and subtending an angle (measured in radians) with the circle center — i.e., the central angle — equals . This is because

Substituting in the circumference

and, with being the same angle measured in degrees, since the arc length equals

A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

ARC21

ARC21 is a local government body in Northern Ireland that is tasked with coordination of the waste management services in the North East of Northern Ireland. The ARC21 waste management region includes the city, borough and district councils of:

ARC21 is accountable to the Northern Ireland Department for the Environment.

See also

References

Charisma (disambiguation)

Charisma is either compelling attractiveness or charm that can inspire devotion in others, or a divinely conferred power or talent.

Charisma or Charismatic may also refer to:

Religion

Arts and entertainment

Plants and animals

See also

Charisma (horse)

Charisma (1972 - 2003) was a horse ridden by New Zealander Mark Todd. Charisma won many competitions in the sport of eventing. He is considered by many to be one of the greatest event horses ever to have competed. He stood 14.3 hands (59 inches, 150 cm).

Breeding and early life

Charisma, also known as "Podge" and "Stroppy," was born October 30, 1972. His 12 hands (48 inches, 122 cm) hand dam, Planet, was by the Connemara and 1/16 Thoroughbred stallion Kiritea. Her dam was a Thoroughbred mare named Starbourne. Planet was a very successful Grade A show jumper in New Zealand, and under rider Sheryl Douglas, became the first mare in New Zealand to jump her own height. However, an injury ended her career, and she went home and was bred to the Thoroughbred stallion, Tira Mink.

Charisma's first home was on the William's 3,000-acre (12 km²) farm in Wairarapa. Even at a young age, Charisma was laid-back and easy to train. He was soon bought by David Murdoch, who placed the yearling in a small pasture with a four-foot fence, which Charisma jumped. The colt was gelded as a four-year-old, although he managed to cover four mares before that time.

Ulmus 'Morton Glossy' Triumph

Ulmus 'Morton Glossy' (selling name Triumph™) is a hybrid cultivar originally named 'Charisma' until it was realized that name had already been registered for another plant. The tree was derived from a crossing of two other hybrid cultivars grown at the Morton Arboretum: Accolade and Vanguard.

Description

Triumph has been promoted in the USA as "strong and symmetrical" in growth and habit . However, its performance in the southern United States has not impressed, and it was dismissed as "ugly" by Michael Dirr, Professor of Horticulture at the University of Georgia , on account of its "wild" growth and splaying branches. It is similar in stature to the American Elm and has leaves that are a deep glossy green when mature, < 10 cm in length by 5 cm broad, with rough upper surface and finely toothed margins. In trials in the UK, Triumph was found to be the first elm to flush in spring, and the first to shed its leaves in the fall, usually by early October. In commerce, the tree is propagated by grafting onto an Ulmus pumila rootstock.

Opposition (Altars EP)

Opposition is the first extended play from Altars. Strike First Records released the album on July 19, 2011.

Critical reception

Awarding the album three and a half stars from Jesus Freak Hideout, Josh Taylor states, "it's really a testament to the integrity and talent of Altars that Opposition is as solid as it is." Graeme Crawford, rating the album a seven out of ten for Cross Rhythms, writes, "But at the moment, there is maybe not enough here to stand out from the crowd." Giving the album four stars at Indie Vision Music, BMer says, "Opposition is a powerful, passionate release". Brian Morrissette, awarding the album three stars for Christ Core, describes, "Great debut EP from a young band still developing their own sound." Rating the album a seven out of ten from Mind Equal Blown, Maria Gironas states, "Truly shows how passionate the Altars are about spreading their message of their Faith."

Track listing

References