You can get to this same result using calculus if you imagine dividing up your annulus into many many annuli (very thin donuts) with an infinitesimal width. In the following image, the large ring has a radius of 4 and the smaller ring has a radius of 2: If the radius of the larger circle is R and the radius of the smaller circle is r, the radius of the circle will be π(R 2 – r 2).
To calculate the area, think about the shape as a larger circle with a smaller circle taken out of it. In the image below, the center of mass is labeled as “C”. The center of mass for an annulus is not within the shape, but at the shared center of both circles. This flat donut shape, or washer, is important for many engineering applications.
The annulus is the region between two concentric rings-two circles that share the same center.
A punctured disk can also be written in terms of a Laurent series. The puncture prevents a closed curve around the region from contracting to a point while keeping within the region (MIT). Although punctured disks are sometimes described as an open annulus, the disks themselves are neither closed sets nor open sets,. The radius can be any positive number when R is infinity, the region is usually called a punctured plane (Sarason, 2007).Ī few interesting features of punctured disks: The region is defined by two inequalities Describing the Punctured DiskĪ punctured disk can be described as an open annulus with center x 0 and an inner radius of zero. Punctured disks arise in complex analysis when studying functions that are well-behaved except for a central point, where there may be an isolated singularity. Disks can also be punctured more than once (Beardon, 1983), so you may see them described as once-punctured or twice punctured. This makes sense when you think of a black hole, which is a gravitational singularity with an enormous mass in an infinitely small space. For example Nevanlinna (1970) regarded the point of puncture as when a boundary curve shrinks to a single point. However, there is more than one definition. More technically, this type of disk is an annulus (a flat donut) with an inner radius of zero, i.e. Punctured open disk around z 0(left) Open disk around z 0 (right).
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