- published: 06 Jan 2015
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A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle, which is in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the "radius" of the sphere. The maximum straight distance through the sphere is known as the "diameter" of the sphere. It passes through the center and is thus twice the radius.
In mathematics, a careful distinction is made between the sphere (a two-dimensional surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior).
In 3 dimensions, the volume inside a sphere (that is, the volume of a ball) is given by the formula
where r is the radius of the sphere and π is the constant pi. This formula was first derived by Archimedes, who showed that the volume of a sphere is 2/3 that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.) In modern mathematics, this formula can be derived using integral calculus, i.e. disk integration to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked centered side by side along the x axis from x = 0 where the disk has radius r (i.e. y = r) to x = r where the disk has radius 0 (i.e. y = 0).
Travel is the movement of people or objects (such as airplanes, boats, trains and other conveyances) between relatively distant geographical locations.
The term "travel" originates from the Old French word travail. The term also covers all the activities performed during a travel (movement). A person who travels is spelled "traveler" in the United States, and "traveller" in the United Kingdom.[citation needed]
"The World is a book, and those who do not travel read only a page."
Reasons for traveling include recreation,tourism or vacationing,research travel for the gathering of information, for holiday to visit people, volunteer travel for charity, migration to begin life somewhere else, religious pilgrimages and mission trips, business travel,trade,commuting, and other reasons, such as to obtain health care or fleeing war or for the enjoyment of traveling. Travel may occur by human-powered transport such as walking or bicycling, or with vehicles, such as public transport, automobiles, trains and airplanes.