MathDB

2

Part of 1995 Bundeswettbewerb Mathematik

Problems(2)

locus of third vertices of equilateral triangles

Source: 1994 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

1/27/2020
A line gg and a point AA outside gg are given in a plane. A point PP moves along gg. Find the locus of the third vertices of equilateral triangles whose two vertices are AA and PP.
geometryLocusEquilateral
union of finitely many disjoint subintervals of [0,1], total length <= 1/2

Source: 1995 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p2

1/27/2020
Let SS be a union of finitely many disjoint subintervals of [0,1][0,1] such that no two points in SS have distance 1/101/10. Show that the total length of the intervals comprising SS is at most 1/21/2.
intervalcombinatoricsunion