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