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Circular Point at Infinity


The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular points at infinity belong to the lines with slopes i and -i. In the plane of a triangle, the circular points at infinity are isogonal conjugates of each other.

All conics passing through the circular points at infinity are circles.

The circular points at infinity are the fixed points of the orthogonal involution.

Circular points at infinity were first considered by Poncelet in 1813 (Coxeter 1993).


See also

Isotropic Line, Point at Infinity

This entry contributed by Floor van Lamoen

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References

Coxeter, H. S. M. The Real Projective Plane, 3rd ed. Cambridge, England: Cambridge University Press, 1993.

Referenced on Wolfram|Alpha

Circular Point at Infinity

Cite this as:

van Lamoen, Floor. "Circular Point at Infinity." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CircularPointatInfinity.html

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