Area of an Annulus
– The area of an annulus is given by the formula A = π(R^2 – r^2).
– The area can also be obtained via calculus by integrating 2πρ dρ from r to R.
– The area of an annulus sector of angle θ is given by A = (θ/2)(R^2 – r^2).
– The area of an annulus is determined by the length of the longest line segment within the annulus, which is the chord tangent to the inner circle.
– The area bounded by the circumcircle and incircle of every unit convex regular polygon is π/4.
Complex Structure of an Annulus
– In complex analysis, an annulus in the complex plane is defined as the region between two concentric circles.
– The complex structure of an annulus depends only on the ratio of the radii.
– Each annulus can be holomorphically mapped to a standard one centered at the origin and with outer radius 1.
– The Hadamard three-circle theorem is a statement about the maximum value a holomorphic function may take inside an annulus.
– The Joukowsky transform conformally maps an annulus onto an ellipse with a slit cut between foci.
Related Concepts
– Annular cutter – a form of core drill.
– Annulus theorem/conjecture – a mathematical concept related to the region between two well-behaved spheres.
– List of geometric shapes.
– Spherical shell – the difference quantity of two concentric balls with varying radius.
– Torus – a doughnut-shaped surface of revolution.
References
– Haunsperger, Deanna; Kennedy, Stephen (2006). ‘The Edge of the Universe: Celebrating Ten Years of Math Horizons’. ISBN 9780883855553.
– [Reference not provided]
External Links
– Annulus definition and properties with interactive animation.
– Area of an annulus formula with interactive animation.
– Compact topological surfaces and their immersions in 3D.
– Wiktionary definition of annulus.
– [Link not provided] Source: https://en.wikipedia.org/wiki/Annulus_(mathematics)
In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word anulus or annulus meaning 'little ring'. The adjectival form is annular (as in annular eclipse).
The open annulus is topologically equivalent to both the open cylinder S1 × (0,1) and the punctured plane.
