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Article: Diameter


Definition and Properties of Diameter

  • A diameter is a straight line segment that passes through the center of a circle or sphere.
  • It is the longest chord of a circle.
  • The length of a diameter is twice the length of the radius.
  • In a convex shape, the diameter is the largest distance between two opposite parallel lines tangent to its boundary.
  • For an ellipse, a diameter is any chord passing through the center of the ellipse.

Generalizations of Diameter

  • The concept of diameter extends beyond circles, spheres, and convex shapes.
  • It can be defined for any n-dimensional object, such as a hypercube or a set of scattered points.
  • The diameter of a subset in a metric space is the least upper bound of all distances between pairs of points in the subset.
  • The diameter of the empty set is either considered as negative infinity or zero, depending on the context.
  • The diameter of a solid object or set of scattered points is the same as the diameter of its convex hull.

Symbol for Diameter

  • The symbol ⌀ is used in technical drawings or specifications to represent diameter.
  • It can be used as a prefix or suffix for a number to indicate diameter (e.g., ⌀ 55 mm).
  • In Windows, the symbol ⌀ can be entered using Alt code 8960.
  • The symbol ⌀ is not included in the dim.shx font, but it is available in other fonts.
  • The wasysym package provides support for the symbol ⌀ in LaTeX.

Diameter vs. Radius

  • The diameter of a circle is exactly twice its radius.
  • This relationship holds true only for circles and in the Euclidean metric.
  • Jungs theorem provides more general inequalities relating the diameter to the radius.
  • The radius is the distance from the center of a circle to any point on its circumference.
  • The diameter is the distance between two points on the circumference passing through the center.

Related Concepts and References

  • Angular diameter refers to how large a sphere or circle appears.
  • Caliper and micrometer are tools used for measuring diameters.
  • Conjugate diameters are perpendicular diameters of a circle or hyperbolic-orthogonal diameters of a hyperbola.
  • Diameter in group theory measures the complexity of a finite group.
  • Eratosthenes calculated the diameter of the Earth around 240 BC.

Diameter Data Sources

Reference URL
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