A hyperbola is a plane curve, one of the conic sections, formed by a plane that cuts both nappes of a right circular cone but does not pass through the vertex of the cone. A hyperbola has two U- shaped non-intersecting branches, identical in form, with the open parts facing in opposite directions; the arms of each branch separate as they recede. A hyperbola is also defined as the locus of all points, such that the difference between the distances from any point on the hyperbola to two fixed points, called the foci, is equal to a constant. Each branch contains one focus in its interior area; the line joining the foci intersects each branch in a point called a vertex. This line, or the segment between the vertices, is called the transverse axis. The line perpendicular to the transverse axis and passing through the point midway between the vertices, midway between the foci, is the conjugate axis. The two axes meet at the centre of the hyperbola, which is symmetric with respect to each axis and the centre.
A hyperbola has two asymptotes passing through the centre; an asymptote of a curve is a straight line with the property that the distance between it and the curve approaches zero as the curve recedes to infinity. A rectangular or equilateral hyperbola has asymptotes that are perpendicular to each other. The hyperbola has useful and important properties. In particular, the angle formed at a point on the hyperbola by the lines joining the point to the foci is bisected by the tangent to the hyperbola at that point. In astronomy, some orbits are hyperbolic in shape. The modern navigational device the loran also uses
hyperbolas. Research Hyperbola
In cartography, projections are ways of representing the earth's surface on a map. Because the earth is round, any map distorts the area it represents (just as flattening out an orangepeel distorts its original shape). Only a globe can be really accurate. Different types of projection have been worked out, each suited to a particular purpose. The two main ones are Conical and Cylindrical. The former shows each hemisphere as a cone which has been unrolled. A Cylindrical Projection shows the earth as though it were an unrolled cylinder. Mercator's projection is cylindrical. Its main fault is that it makes the Equator out to be the same length as all other latitudes, even those near the Poles, which are really only a few miles long. Thus countries near the Poles appear far larger than they really are. Research Projections
The Alaudidae are the Lark family of Conirostral birds. They are characterized by a bill forming an elongated cone, the mandibles of equal length, the upper convex, slightly curved. The nostrils are at the base of the bill, oval, and partly covered by small feathers directed forwards. The feathers of the head are capable of being erected so as to form a crest. The first primary is very short, the second shorter than the third which is the longest in the wing. The toes are divided to the base. The hind claw is nearly straight and longer than the toes. They are granivorous birds, frequenting open fields, and singing during their flight. They nest and feed on the ground. They take dust baths instead of water baths. Research Alaudidae
The branchiogasteropoda are gasteropodous molluscs whose respiration is aquatic, being generally effected by means of external branchiae or gills. They include a great many animals with univalve shells, as whelks, limpets, cone-shells, periwinkles, cowries, etc, also sea-hares, sea-slugs, sea-lemons, and the heteropoda. Research Branchiogasteropoda
In botany, a cone is a dry compound fruit, consisting of many open scales, each with two seeds at the base, as in the conifers; also called a strobile or strobilus. Research Cone
Coniferae (the Conifers) are the pines, firs, and their allies, a natural order of gymnospermous exogens, the essential character of which consists in the manner in which the ovules, not inclosed in an ovary, receive directly the action of the pollen without the intervention of a stigma. The ovules in these plants are borne on scales or modified leaves, which are spread out, not folded, and generally grouped in such a manner as to form a cone composed of a greater or smaller number of these leaves, of which only a portion may be fertile and bear ovules. The disposition, of the ovules in relation to these scales permits of a division of the Coniferae into three distinct families or tribes.
In the Cupressineae, which include the juniper, cypress, etc, the cones are formed of simple scales, each of which bears towards the base of its superior surface the ovules erect and sessile.
The second family, Abietineae, has in place of simple scales, scales actually double or formed of two parts; the lower one usually designated the bract; the other bearing at its base the ovules reversed. This family includes the pines, firs, and larches, the araucarias, Wellingtonias, dammaras, etc. In these two families the ovules are completely covered by the scales which constitute the cones, which unite after fecun-dation, and inclose the seedtill their maturity.
In the Taxineae, which constitute the third family, the scales are short, imperfect, and partly sterile, and neither cover the ovules at the period of fecundation nor at that of maturation. The ovules are usually set in the same manner as in the Cupressineae. The yew, the gingko, etc, belong to this family.
The Conifers are found in large forests in the north of Europe and America, and are of great importance as timber trees. They abound also in resinous juices and yield turpentine, pitch, tar, succinic acid, etc. The leaves are usually alternate, and awl or needle shaped, the naked flowers are monoecious or dioecious, the male flowers being in deciduous catkins, the female in cones. Research Coniferae
Cypress is a genus of coniferous (evergreen) cone-bearing trees and shrubs, with small adnate opposite leaves, and small globular cones on a few fleshy scale-leaves. The Capressus sempervirens, or common European cypress, is a dark-coloured evergreen with extremely small leaves, entirely covering the branches. It has a quadrangular, or, where the top branches diminish in length, pyramidal shape. Cypress-trees, though of a somewhat sombre and gloomy appearance, may be used with great effect in shrubberies and gardens. They are much valued also on account of their wood, which is hard, compact, and very durable, of a reddish colour and a pleasant smell. It was used at funerals and as an emblem of mourning by the ancients. Amongst other members of the genus are the Indian cypress (Cypress glauca); the Cypress pendula, a native of China and Japan; and the Cypress thurifera, or incense-bearing cypress, a native of Mexico; the evergreen American cypress or White Cedar (Cypress thyoides); etc. The Taxodium distichum, or deciduous cypress of the United States and Mexico, is frequently called the Virginian cypress. Its timber is valuable, and under water is almost imperishable. Research Cypress
Dentalium is a genus of gasteropodous molluscs, the shell of which consists of a tubular arcuated cone open at both ends, and resembling the tusk of an elephant in miniature. There are many species, known by the common name of tooth-shells. Research Dentalium
Ephedra (Ephedra vulgaris), also known as Ephedrine, Epitonin and Ma Huang, is an Asiatic plant of the order Gnetaceae found on sandy seashores in temperate climates of both hemispheres in China, Siberia and Japan. The plant has stamens and pistils on separate flowers, the staminate flowers occurring in catkins and a membranous perianth, pistillate flowers occurring terminal on axillary stalks within a two-leaved involucre. The fruit has two carpels with a single seed in each and is a succulentcone. The plant's branches are slender and erect with small leaves which are scale-like, articulated and joined at the base into a sheaf. The plant contains Ephedrine, a sympathetic nervestimulant resembling adrenaline and has antispasmodic properties. Research Ephedra
The Probert Encyclopaedia was designed, edited and programed by
Matt and Leela Probert
Abbreviations
Research Hyperbola
