Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal ; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
The A470 is a trunk road in Wales. It is the country's longest road at 186 miles (299 km) and links the capital Cardiff on the south coast to Llandudno on the north coast. While previously one had to navigate the narrow roads of Llanidloes and Dolgellau, both these market towns are now bypassed due to extensive road modernisation. The 26 miles (42 km) from Cardiff Bay to Merthyr Tydfil are mainly dual carriageway, but most of the route from north of Merthyr to Llandudno is single carriageway.
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four straight sides of equal length and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°). A square with vertices ABCD would be denoted ABCD.
The Taff Trail is a walking and cycle path that runs for 55 miles (89 km) between Cardiff Bay and Brecon in Wales. It is so named because it follows the course of the River Taff. Along much of its length, it follows the National Cycle Network Route 8 that continues to Holyhead, and is substantially off-road.
Selwyn is a village in the Selwyn District of Canterbury, New Zealand. It was laid out in the 1860s for a population of 2,000 people, but it currently has very few houses.
Dovedale is a valley in the Peak District of England. The land is owned by the National Trust and attracts a million visitors annually. The valley was cut by the River Dove and runs for just over 3 miles (5 km) between Milldale in the north and a wooded ravine, near Thorpe Cloud and Bunster Hill, in the south. In the wooded ravine, a set of stepping stones cross the river and there are two caves known as the Dove Holes.
Llanelwedd is a village and community near Builth Wells, in Powys, Wales. It lies within the historic boundaries of Radnorshire. Llanelwedd features the Royal Welsh Showground.
A miter joint is a joint made by cutting each of two parts to be joined, across the main surface, usually at a 45° angle, to form a corner, usually to form a 90° angle, though it can comprise any angle greater than 0 degrees. It is called beveling when the angled cut is done on the side, although the resulting joint is still a miter joint.
Penrhyndeudraeth is a small town and community in the Welsh county of Gwynedd. The town is close to the mouth of the River Dwyryd on the A487 nearly 3 miles (4.8 km) east of Porthmadog, and had a population of 2,150 at the 2011 census, increased from 2,031 in 2001. The community includes the villages of Minffordd and Portmeirion.
A pier, in architecture, is an upright support for a structure or superstructure such as an arch or bridge. Sections of structural walls between openings (bays) can function as piers. External or free-standing walls may have piers at the ends or on corners.
Burland is a village and former civil parish, now in the parish of Burland and Acton, in the unitary authority area of Cheshire East and the ceremonial county of Cheshire, England, about 2+1⁄2 miles west of Nantwich. The civil parish also included the small settlements of Burland Lower Green, Burland Upper Green, Hollin Green and Stoneley Green, as well as parts of Gradeley Green and Swanley. The eastern part of the village of Ravensmoor also falls within the civil parish.
Raglan (; is a village and community in Monmouthshire, south-east Wales, United Kingdom. It is located some 9 miles south-west of Monmouth, midway between Monmouth and Abergavenny on the A40 road very near to the junction with the A449 road. It is the location of Raglan Castle, built for William ap Thomas and now maintained by Cadw. The community includes the villages of Llandenny and Pen-y-clawdd. Raglan itself has a population of 1,183.
Blackstone is a hamlet in the civil parish of Woodmancote and the Horsham district of West Sussex, England. Blackstone is significant for its listed 17th- and 18th-century houses and cottages.
Mengkuang Titi is a village within the city of Seberang Perai in the Malaysian state of Penang. It is located not too far from the Mengkuang Dam. The village has a population of about 800, and still retains the rustic feel ideal for the development of agricultural and cottage industries.
State Road 247 is a southwest to northeast state highway between U.S. Route 129 in Branford, Suwannee County, Florida and US 90 in Lake City, Columbia County, Florida. It is almost entirely a two-lane undivided highway except at its termini, and some intersections, where it contains left-turn lanes. Between its termini, SR 247 intersects with no state roads other than former ones.
Glantwymyn is a community in the northwest (Montgomeryshire) of Powys, Wales.
