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The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, ... An ellipse with an aspect ratio of 1:1 is a circle.
The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is f = a − b a . {\displaystyle f={\frac {a-b}{a}}.} The compression factor is b / a {\displaystyle b/a} in each case; for the ellipse, this is also its aspect ratio .
Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It is denoted here by α (alpha). It may be defined in terms of the eccentricity , e , or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis ):
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The aspect ratio of an oblate spheroid/ellipse, c : a, is the ratio of the polar to equatorial lengths, while the flattening (also called oblateness) f, is the ratio of the equatorial-polar length difference to the equatorial length: = =.
The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it: = The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an equiaxed grain.
The eccentricity of an ellipse is, most simply, the ratio of the linear eccentricity c (distance between the center of the ellipse and each focus) to the length of the semimajor axis a. =. The eccentricity is also the ratio of the semimajor axis a to the distance d from the center to the directrix:
Cylindrical equal-area projection with standard parallels at 30°N/S and an aspect ratio of (3/4)π ≈ 2.356. 2002 Hobo–Dyer: Cylindrical Equal-area Mick Dyer: Cylindrical equal-area projection with standard parallels at 37.5°N/S and an aspect ratio of 1.977. Similar are Trystan Edwards with standard parallels at 37.4° and Smyth equal ...