radius

mathematics

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July 13, 2026

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In geometry, a radius is a line segment that extends from the center of a circle or sphere to its circumference or bounding surface. It is also defined as the distance from a fixed point to a variable point. The length of this segment is crucial in determining a circle's or sphere's properties.12

For a circle, the radius, when multiplied by (\pi), gives the distance around the circle (circumference), and when squared and multiplied by (\pi), it yields the circle's area. For a sphere, the surface area is calculated as (4\pi r^2), and its volume is (\frac{4}{3}\pi r^3), where 'r' represents the radius. The concept of the radius is fundamental in Euclidean and elliptic geometry.34

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mechanics
Circular motion
…be specified by giving the radius r of the circle and the angle θ between the position vector and the x-axis. Although r is constant, θ increases uniformly with time t, such that θ = ωt, or dθ/dt = ω, where ω is the angular frequency in equation (26). Contrary…
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…be specified by giving the radius r of the circle and the angle θ between the position vector and the x-axis. Although r is constant, θ increases uniformly with time t, such that θ = ωt, or dθ/dt = ω, where ω is the angular frequency in equation (26). Contrary…
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Hipparchus
Solar and lunar theory
…Earth is 77 times Earth’s radius. In the second method he hypothesized that the distance from the centre of Earth to the Sun is 490 times Earth’s radius—perhaps chosen because that is the shortest distance consistent with a parallax that is too small for detection by the unaided eye. Using…
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…Earth is 77 times Earth’s radius. In the second method he hypothesized that the distance from the centre of Earth to the Sun is 490 times Earth’s radius—perhaps chosen because that is the shortest distance consistent with a parallax that is too small for detection by the unaided eye. Using…
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sound
The inverse square law
…inverse relationship with the growing radius of the circle, or distance from the source of the wave. In the same way, as a spherical wave front expands, its energy is distributed over a larger and larger surface area. Because the surface area of a sphere is proportional to the square…
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…inverse relationship with the growing radius of the circle, or distance from the source of the wave. In the same way, as a spherical wave front expands, its energy is distributed over a larger and larger surface area. Because the surface area of a sphere is proportional to the square…
Read More