# Diameter

**Ddiameters⌀ØDiameter of a point setdiametricallycalibrediaDia'''meterdia.**

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.wikipedia

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### Sphere

**sphericalhemisphereglobose**

Both definitions are also valid for the diameter of a sphere.

The longest straight line segment through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of both the sphere and its ball.

### Circle

**circularcircles360 degrees**

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.

The ratio of a circle's circumference to its diameter is irrational constant approximately equal to 3.141592654.

### Chord (geometry)

**chordchords chord**

It can also be defined as the longest chord of the circle.

Every diameter is a chord, but not every chord is a diameter.

### Conjugate diameters

**conjugate diameterBounding parallelogramconjugate**

For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one of them is parallel to the other one.

In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter.

### Rotating calipers

**rotating caliper**

Both quantities can be calculated efficiently using rotating calipers.

In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.

### Radius

**radiiradialradially**

In this sense one speaks of the diameter rather than a diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r.

By extension, the diameter d is defined as twice the radius:

### Semi-major and semi-minor axes

**semi-major axissemimajor axissemi-major axes**

The longest diameter is called the major axis.

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

### Reuleaux triangle

**spherical triangleReuleaux polygonReuleaux heptagon**

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite that can be inscribed into a Reuleaux triangle.

### Curve of constant width

**curves of constant widthconstant diameterconstant width**

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

A basic result on curves of constant width is Barbier's theorem, which asserts that the perimeter of any curve of constant width is equal to the width (diameter) multiplied by π.

### Line segment

**segmentline segmentssegments**

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.

Any chord in a circle which has no longer chord is called a diameter, and any segment connecting the circle's center (the midpoint of a diameter) to a point on the circle is called a radius.

### Metric space

**metricmetric spacesmetric geometry**

The diameter of a subset of a metric space is the least upper bound of the set of all distances between pairs of points in the subset.

The smallest possible such r is called the diameter of M.

### Invariant (mathematics)

**invariantinvariantsinvariance**

In differential geometry, the diameter is an important global Riemannian invariant.

As another example, all circles are similar: they can be transformed into each other and the ratio of the circumference to the diameter is invariant (denoted by the Greek letter pi).

### Phi

**ΦPhi (letter)Φ φ**

The diameter symbol ⌀ is distinct from the empty set symbol ∅, from an (italic) uppercase phi Φ, and from the Nordic vowel Ø.

### Convex hull

**closed convex hullconvex envelopeX Form Hull**

For any solid object or set of scattered points in n-dimensional Euclidean space, the diameter of the object or set is the same as the diameter of its convex hull.

It also serves as a tool, a building block for a number of other computational-geometric algorithms such as the rotating calipers method for computing the width and diameter of a point set.

### Ø

**Ǿslashed o**

The diameter symbol ⌀ is distinct from the empty set symbol ∅, from an (italic) uppercase phi Φ, and from the Nordic vowel Ø. It is similar in size and design to ø, the Latin small letter o with stroke.

### Jung's theorem

In geometry, Jung's theorem is an inequality between the diameter of a set of points in any Euclidean space and the radius of the minimum enclosing ball of that set.

### Semidiameter

**semi-diameter**

In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.

### Photographic filter

**Filterfiltersphotographic filters**

For example, photographic filter thread sizes are often denoted in this way.

The filter diameter for a particular lens is commonly identified on the lens face by the ⌀ symbol.

### Sauter mean diameter

**Sauter diameter**

It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest.

### Ø (disambiguation)

**diagonal line through the Oother symbols**

### Circumscribed circle

**circumcirclecircumcentercircumradius**

The diameter of the circumcircle, called the circumdiameter and equal to twice the circumradius, can be computed as the length of any side of the triangle divided by the sine of the opposite angle:

### Geometry

**geometricgeometricalgeometries**

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.

### Convex set

**convexconvex subsetconvexity**

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is often defined to be the smallest such distance.

### Parallel (geometry)

**parallelparallel linesparallelism**

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is often defined to be the smallest such distance.