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Everything about Ellipsoid

Quadric surface that looks like a deformed sphere

An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: EllipsoidA 5-minute orientation
  2. Skim a recent paper: A Novel Interval Power Flow Method Based on Hybrid Box-Ellipsoid Uncertain SetsInfluential work since 2022
  3. Pick up a classic book: A history of the mathematical theories of attraction and the figure of the earth from the time of Newton to that of LaplaceThe most-reprinted book on the subject
  4. Read the landmark paper: Demagnetizing Factors of the General EllipsoidCited 2,181 times
  5. Go sideways: Confocal conic sectionsA closely related topic
  6. Go sideways: SpheroidA closely related topic

📖 Definitions

Noun A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x/a + y/b + z/c = 1.

Noun Such a surface used as a model of the shape of the earth.

Adjective Shaped like an ellipse; elliptical.

Adjective Of or pertaining to an ellipse; elliptic.

🗂️ The subject at a glance

  1. Standard equation
  2. Parameterization
  3. Volume
  4. Surface area
  5. Plane sections
  6. Pins-and-string construction
  7. In higher dimensions and general position
  8. Applications

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics