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The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let , , , and be four arbitrary points in a plane. Draw an arbitrary plane through each of the six lines through pairs of points . The set of three of these planes , , passing through the pairs from three of the original points meet in a point . The theorem of Möbius tetrads then states that the four points , , , and lie in a plane (Baker 1992, p. 62).

Coplanar, Möbius Tetrahedra, Pappus's Hexagon Theorem

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## References

Baker, H. F. Principles of Geometry, Volume 1: Foundations. Cambridge, England: pp. 61-62, 1922.Baker, H. F. Principles of Geometry, Volume 4: Higher Geometry. Cambridge, England: pp. 18-21, 1925.Möbius, F. A. "Kann von zwei dreiseitigen Pyramiden eine jede in Bezug auf die andere um- und eingeschrieben zugleich heissen?" J. reine angew. Math. 3, 273-278, 1828.National Museum of American History. "Model of Moebius's Theorem by Richard P. Baker, Baker #432a." https://americanhistory.si.edu/collections/search/object/nmah_1087015.National Museum of American History. "Model of Moebius's Theorem, by Richard P. Baker, Baker #432b." https://americanhistory.si.edu/collections/search/object/nmah_1087020.

## Cite this as:

Weisstein, Eric W. "Möbius Tetrad Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MoebiusTetradTheorem.html