geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, the semidiameter or semi-diameter of a

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

of points may be one half of its

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...

; or, sometimes, one half of its extent along a particular direction.

Special cases

The semi-diameter of a

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is con ...

, or interval is the same thing as its

radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

— namely, any line segment from the

center Center or centre may refer to: Mathematics *Center (geometry), the middle of an object * Center (algebra), used in various contexts ** Center (group theory) ** Center (ring theory) * Graph center, the set of all vertices of minimum eccentrici ...

to its

boundary Boundary or Boundaries may refer to: * Border, in political geography Entertainment * ''Boundaries'' (2016 film), a 2016 Canadian film * ''Boundaries'' (2018 film), a 2018 American-Canadian road trip film *Boundary (cricket), the edge of the pla ...

. The semi-diameters of a non-circular ellipse are the halves of its extents along the two

axes of symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

. They are the parameters ''a'', ''b'' of the

implicit equation In mathematics, an implicit equation is a relation of the form R(x_1, \dots, x_n) = 0, where is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is x^2 + y^2 - 1 = 0. An implicit func ...

\left(\frac\right)^+\left(\frac\right)^=1.\,\!

Likewise, the semi-diameters of an ellipsoid are the parameters ''a'', ''b'', and ''c'' of its implicit equation :

\left(\frac\right)^+\left(\frac\right)^+\left(\frac\right)^{2}=1.\,\!

The semi-diameters of a superellipse,

superellipsoid In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same exponent ''r'', and whose vertical sections through the center are superellipses with the same exponent '' ...

, or

superquadric In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary po ...

can be identified in the same way.

Special cases

See also