radius

Dictionary: ra·di·us (rā'dē-əs) pronunciation

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radius

(Carlyn Iverson)

n., pl. -di·i (-dē-ī') or -di·us·es.

(Abbr. r or rad.) Mathematics.
1. A line segment that joins the center of a circle with any point on its circumference.
2. A line segment that joins the center of a sphere with any point on its surface.
3. A line segment that joins the center of a regular polygon with any of its vertices.
4. The length of any such line segment.
A circular area measured by a given radius: every family within a radius of 25 miles of the city center.
A bounded range of effective activity or influence: the operating radius of a helicopter.
A radial part or structure, such as a mechanically pivoted arm or the spoke of a wheel.
Anatomy.
1. A long, prismatic, slightly curved bone, the shorter and thicker of the two forearm bones, located on the lateral side of the ulna.
2. A similar bone in many vertebrates.

[Latin, ray, spoke of a wheel, radius.]

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Sports Science and Medicine: radius

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1. A bone of the forearm. The radius is shorter than the ulna and, in the anatomical position, lies laterally on the thumb side.

2. A line extending front the centre to the circumference of a circle.

Veterinary Dictionary: radius

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Pl. radii [L.]
1. a line radiating from a center, or a circular limit defined by a fixed distance from an established point or center.
2. one of the two long bones of the forearm that extends from the lateral side of the elbow to the medial side of the wrist or carpus.

r. curvus syndrome — see curvus.

Word Tutor: radius

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IN BRIEF: Any straight line that goes from the center to the outside of a circle or sphere. Also: The thicker of the two bones in the forearm.

Every radius of a circle measures exactly the same.

Wikipedia: Radius

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For other uses, see Radius (disambiguation).

Circle illustration

In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

More generally — in geometry, science, engineering, and many other contexts — the radius of something (e.g., a cylinder, a polygon, a mechanical part, or a galaxy) usually refers to the distance from its center or axis of symmetry to its outermost points. If the object does not have an obvious center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter (which is usually defined as the maximum distance between any two points of the figure).

The radius of a regular polygon (or polyhedron) is the distance from its center to any of its vertices; which is also its circumradius.

In graph theory, the radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph.

The name comes from Latin radius, meaning "ray" but also the spoke of a chariot wheel. The plural in English is radii (as in Latin), but radiuses is also occasionally used.

1 Formulas for circles
2 Formulas for regular polygons
- 2.1 Radius from side
3 Formulas for hypercubes
- 3.1 Radius from side
4 See also

Formulas for circles

Radius from circumference

The radius of the circle with perimeter (circumference) C is

$r = \frac{C}{2\pi}.$

Radius from area

The radius of a circle with area A is

$r= \sqrt{\frac{A}{\pi}}.$

Radius from three points

To compute the radius of a circle going through three points P₁, P₂, P₃, the following formula can be used:

$r=\frac{|P_1-P_3|}{2\sin\theta}$

where θ is the angle $\angle P_1 P_2 P_3.$

Formulas for regular polygons

These formulas assume a regular polygon with n sides.

Radius from side

The radius can be computed from the side s by:

$r = R_n\, s$ where $R_n = \frac{1}{2 \sin \frac{\pi}{n}} \quad\quad \begin{array}{r|ccr|c} n & R_n & & n & R_n\\ \hline 2 & 0.50000000 & & 10 & 1.6180340- \\ 3 & 0.5773503- & & 11 & 1.7747328- \\ 4 & 0.7071068- & & 12 & 1.9318517- \\ 5 & 0.8506508+ & & 13 & 2.0892907+ \\ 6 & 1.00000000 & & 14 & 2.2469796+ \\ 7 & 1.1523824+ & & 15 & 2.4048672- \\ 8 & 1.3065630- & & 16 & 2.5629154+ \\ 9 & 1.4619022+ & & 17 & 2.7210956- \end{array}$

Formulas for hypercubes

Radius from side

The radius of a d-dimensional hypercube with side s is

$r = \frac{s}{2}\sqrt{d}.$

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Copyrights:

		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
		Sports Science and Medicine. The Oxford Dictionary of Sports Science & Medicine. Copyright © Michael Kent 1998, 2006, 2007. All rights reserved. Read more
		Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved. Read more
		Word Tutor. Copyright © 2004-present by eSpindle Learning, a 501(c) nonprofit organization. All rights reserved. eSpindle provides personalized spelling and vocabulary tutoring online; free trial. Read more
		Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Radius". Read more
		Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved. Read more

Atec Radius Pitching Machine	Lacoste Mens Radius
Lacoste Radius 2 Tone	Radius 2 Tone

radius

Contents

Formulas for circles

Radius from circumference

Radius from area

Radius from three points

Formulas for regular polygons

Radius from side

Formulas for hypercubes

Radius from side

See also