## perpendicular bisector

The perpendicular bisector of a line segment *AB* is the straight line perpendicular to *AB* through the midpoint of *AB*.

## perpendicular bisector Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

... bisector The perpendicular bisector of a line segment AB is the straight line perpendicular to AB through the midpoint of AB...

## bisector Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

... The line that divides an angle into two equal angles. See also internal bisector , external bisector and perpendicular bisector...

## kite Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...A quadrilateral that has two adjacent sides of equal length and the other two sides of equal length. If the kite ABCD has AB = AD and CB = CD , the diagonals AC and BD are perpendicular, and AC bisects BD...

## circumcentre Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...The circumcentre of a triangle is the centre of the circumcircle of the triangle. It is the point O , shown in the figure, at which the perpendicular bisectors of the sides of the triangle are...

## axis of symmetry Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...of symmetry A line in which the mirror image of a curve or geometrical figure maps onto itself. The condition for this is that for each point P on the curve or figure the point P ′ is also, where the axis is the perpendicular bisector of PP...

## pedal triangle Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...triangle In the triangle with vertices A , B , and C , let D , E and F be the feet of the perpendiculars from A , B and C , respectively, to the opposite sides, so that AD , BE and CF are the altitudes . The triangle DEF is called the pedal triangle. The altitudes of the original triangle bisect the angles of the pedal...

## skeletagenous septum Quick reference

### A Dictionary of Zoology (4 ed.)

...septum One of a series of segments which develop along the notochord and are separated by myosepta . Septa occur in two planes. Dorsal and ventral septa are plate-like processes which grow dorsally and ventrally to the notochord; horizontal septa bisect this plane perpendicularly. Mesenchymal cells migrate to the skeletagenous septa during the gastrula stage of embryogenesis to form sclerotomic tissue ( see somite ). At the junction between the myoseptum and skeletagenous septum vertebrae develop; they are consequently intersegmental...

## Thiessen polygon Quick reference

### A Dictionary of Geography (5 ed.)

...polygon A subdivision of a drainage basin, containing a rain gauge. Polygons are constructed by first siting the rain gauges, plotting them on a base map, and connecting the sites by straight lines. The lines are bisected with perpendiculars, which meet to form the polygons. The areas of the polygons are calculated and expressed as fractions of the total area. Each fraction is multiplied by the precipitation recorded by its rain gauge. The sum of these calculations represents total precipitation over the catchment area. For an account, see Yoo et al....

## equidistant Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...Being the same distance from one or more points or objects. The perpendicular bisector of the line segment AB is the set of points equidistant from A and B . The set of points equidistant from a fixed point is a circle in two dimensions and a sphere in three dimensions. The set of points equidistant from a line segment is formed by a pair of parallel line segments with two...

## Brillouin zone Quick reference

### A Dictionary of Chemistry (7 ed.)

...zone A cell in a reciprocal lattice. The first Brillouin zone is the cell of smallest volume enclosed by those planes that are perpendicular bisectors of reciprocal lattice vectors. Higher Brillouin zones also exist. Brillouin zones are used in the theory of energy levels in a periodic potential, as in a crystal. They are named after the French physicist Léon Brillouin ( 1889–1969 ), who introduced them into the theory of crystals in 1930...

## Wigner–Seitz cell Quick reference

### A Dictionary of Chemistry (7 ed.)

...cell A polyhedron in a crystal that is bounded by planes formed by perpendicular bisectors of bonds between lattice sites. The Wigner–Seitz cell was used by Hungarian-born US physicist Eugene Wigner ( 1902–95 ) and Frederick Seitz ( 1911–2008 ) in 1933 in the course of their analysis of the cohesion of metals. The concept has been used extensively in the theory of...

## locus Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...the plane) is the set of all points in the plane that satisfy some given condition or property. For example, the locus of all points that are a given distance from a fixed point is a circle; the locus of all points equidistant from two given points, A and B , is the perpendicular bisector of AB . If, in a given coordinate system, a locus can be expressed in the form {( x , y ),| f ( x , y )=0}, the equation f ( x , y )=0 is called an equation of the locus (in the given coordinate system). The equation may be said to ‘represent’ the...

## Wigner–Seitz cell Quick reference

### A Dictionary of Physics (8 ed.)

...Wigner–Seitz cell A unit cell of a crystal lattice that is constructed by starting from some lattice site and drawing lines to all the neighbouring lattice sites. The region enclosed by the perpendicular bisecting planes of these lines is the Wigner–Seitz cell of the crystal. The concept of the Wigner–Seitz cell was put forward in 1933 by Eugene Wigner and Frederick Seitz ( 1911–2008 ). The same construction in reciprocal space gives the first Brillouin zone , a concept that is very useful in the theory of energy bands . Polyhedra constructed...

## Schoenflies system Quick reference

### A Dictionary of Physics (8 ed.)

...rotation axis, have a mirror plane perpendicular to the axis. S n groups have an n -fold rotation–reflection axis. D n groups have an n -fold rotation axis and a two-fold axis perpendicular to the n -fold axis (and two-fold axes associated with the existence of the n -fold axis). D nh groups have all the symmetry operations of D n and also a mirror plane perpendicular to the n -fold axis. D nd groups contain all the symmetry operations of D n and also mirror planes that contain the n -fold axis and bisect the angles between the two-fold axes....

## Schoenflies system Quick reference

### A Dictionary of Chemistry (7 ed.)

...rotation axis, have a mirror plane perpendicular to the axis. S n groups have an n -fold rotation-reflection axis. D n groups have an n -fold rotation axis and a two-fold axis perpendicular to the n -fold axis (and two-fold axes associated with the existence of the n -fold axis). D nh groups have all the symmetry operations of D n and also a mirror plane perpendicular to the n -fold axis. D nd groups contain all the symmetry operations of D n and also mirror planes that contain the n -fold axis and bisect the angles between the two-fold axes....

## Riparian Long-lot Reference library

### The Oxford Encyclopedia of Latinos and Latinas in the United States

...) were measured in varas—where one vara is equal to about three feet—and were typically one hundred to five hundred feet wide and ten to twenty miles long. The long-lot is somewhat narrow relative to length and in most cases runs perpendicular to water courses. Long-lots in New Mexico and Colorado are usually bisected by community ditches (acequias). Because of the long-lots' reach, the long-lot settlement pattern provides all acequia irrigators with access to the varied topography, plant communities, and water courses of a locality. In the early...

## Maritime Boundaries Reference library

### The Oxford Encyclopedia of Maritime History

...circumstance that has been taken into account is the general direction of the relevant coasts. This basically entails simplifying the coastal configuration by constructing one or more straight lines along these coasts and then drawing a perpendicular—if there is a single line representing all relevant coasts—or a bisector of the angle if there are two intersecting lines representing the general directions of the relevant coasts. The exclusive economic zone and the continental shelf overlap spatially within two hundred nautical miles. Both zones include the...

## Nautical Astronomy and Celestial Navigation Reference library

### The Oxford Encyclopedia of Maritime History

...Wherever the observer stands, the ground is a plane perpendicular to the observer’s body, a plane that extends outward infinitely. The “poles” of the observer are the zenith, the point on the celestial sphere directly overhead, and the nadir, the point directly below the observer, also in a line perpendicular to the horizon plane. A celestial sphere may feature a number of vertical circles. The great circle intersecting the poles and passing through the observer’s zenith is the principal vertical. Perpendicular to the principal vertical, and passing through east...

## Curling Reference library

*Morris MOTT*

### Berkshire Encyclopedia of World Sport (3 ed.)

...to complete all of its throws. They forfeit the match if they fail to do so. Curling Rinks A standard curling rink is between 14.5 and 15 feet wide and at least 146 feet long. As each end is played, only 132 feet of the 146 feet are in play. A centerline bisects the length of the ice, and four perpendicular lines cross the width of the ice at both ends. ( See figure 1 .) The house is centered where the tee line intersects the centerline. The stone must be released before its leading edge touches the near hog line. If a player is still in contact with a stone...

## Navigational Instruments Reference library

### The Oxford Encyclopedia of Maritime History

...Through a complex procedure of bisections and the use of a “scale of equal parts” he was able to lay out angles of 60°, 90°, 75°, and 85°20'. The 85°20' point was the critical step, and it had to be carefully confirmed. Once this point was established it could be bisected into the 1,024 remaining points, dividing the arc into five-minute graduations. An additional series of bisections completed the fifty-six remaining graduations between 85°20' and 90°—a test of skill which very few makers could complete successfully. The Board of Longitude gave Bird an award...