Lesson plan

Angular eccentricity

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 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): : \alpha=\sin^{-1}\!e=\cos^{-1}\left(\frac{b}{a}\right). \,\! Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions. in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp: :: The alternative expressions for the flattenings would guard against large cancellations in numerical work.

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Article summary

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 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): : \alpha=\sin^{-1}\!e=\cos^{-1}\left(\frac{b}{a}\right). \,\! Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions. in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp: :: The alternative expressions for the flattenings would guard against large cancellations in numerical work.

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Discussion questions

  1. Summarise the article in your own words. Which single claim would you verify first, and why?
  2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
  3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

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