BitumenBitumen (ˈbɪtjʊmɪn, bɪˈtjuːmən,_baɪ-) is a sticky, black, highly viscous liquid or semi-solid form of petroleum. In the U.S., it is commonly referred to as asphalt. It may be found in natural deposits or may be a refined product, and is classed as a pitch. Before the 20th century, the term asphaltum was also used. The word is derived from the ancient Greek ἄσφαλτος ásphaltos. The largest natural deposit of bitumen in the world, estimated to contain 10 million tons, is the Pitch Lake in southwest Trinidad.
Asphalt concreteAsphalt concrete (commonly called asphalt, blacktop, or pavement in North America, and tarmac or bitumen macadam in the United Kingdom and the Republic of Ireland) is a composite material commonly used to surface roads, parking lots, airports, and the core of embankment dams. Asphalt mixtures have been used in pavement construction since the beginning of the twentieth century. It consists of mineral aggregate bound together with bitumen (also known as asphalt), laid in layers, and compacted.
SphereA sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry.
Spherical capIn geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere.
Oil sandsOil sands, tar sands, crude bitumen, or bituminous sands, are a type of unconventional petroleum deposit. Oil sands are either loose sands or partially consolidated sandstone containing a naturally occurring mixture of sand, clay, and water, soaked with bitumen, a dense and extremely viscous form of petroleum. Significant bitumen deposits are reported in Canada, Kazakhstan, Russia, and Venezuela. The estimated worldwide deposits of oil are more than ; Proven reserves of bitumen contain approximately 100 billion barrels, and total natural bitumen reserves are estimated at worldwide, of which , or 70.
Road surfaceA road surface (English), or pavement (American), is the durable surface material laid down on an area intended to sustain vehicular or foot traffic, such as a road or walkway. In the past, gravel road surfaces, macadam, hoggin, cobblestone and granite setts were extensively used, but these have mostly been replaced by asphalt or concrete laid on a compacted base course. Asphalt mixtures have been used in pavement construction since the beginning of the 20th century and are of two types: metalled (hard-surfaced) and unmetalled roads.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Spherical segmentIn geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. If the radius of the sphere is called R, the radii of the spherical segment bases are r_1 and r_2, and the height of the segment (the distance from one parallel plane to the other) called h, then the
Spherical conicIn mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant. By taking the antipodal point to one focus, every spherical ellipse is also a spherical hyperbola, and vice versa.
Spherical trigonometrySpherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam.
