TOPICS
Search

Lemoine's Problem


Given the "peaks" of three equilateral triangles placed on the sides of a triangle T, construct T. The problem was proposed by Lemoine (1868) and solved for the general case of isosceles triangles by Kiepert (1869) using the Kiepert hyperbola.


See also

Equilateral Triangle, Isosceles Triangle, Kiepert Hyperbola, Outer Napoleon Triangle

Explore with Wolfram|Alpha

References

Eddy, R. H. and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle." Math. Mag. 67, 188-205, 1994.Kiepert, L. "Solution de question 864." Nouv. Ann. Math. 8, 40-42, 1869.Lemoine, É. "Question 864." Nouv. Ann. Math. 7, 191, 1868.

Referenced on Wolfram|Alpha

Lemoine's Problem

Cite this as:

Weisstein, Eric W. "Lemoine's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemoinesProblem.html

Subject classifications