Line Involution

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two.

If ${AA^',BB^',CC^'}$ is a range in involution, then the ranges ${AA^',BC}$ and ${A^'A,B^'C^'}$ are equicross, and conversely.

Explore with Wolfram|Alpha

More things to try:

30-level 12-ary tree
f'(t) = f(t)^2 + 1
hyperbola with center (100, 200) and focus (110, 180)

References

Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., p. 133, 1888.Lachlan, R. "Theory of Involutions" and "Involution." Ch. 5 and §426-427 in An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 272-274, 1893.

Referenced on Wolfram|Alpha

Line Involution

Cite this as:

Weisstein, Eric W. "Line Involution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LineInvolution.html

Line Involution

See also

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Subject classifications