Three coloured unit disks are placed so that they have a common (3-way) intersection, but none of the disks covers the intersection of the other two disks. What is the minimum radius of the disk that would cover all intersections at once, in all cases?
Cooperation with Marshall W. Buck.
Two points are on opposite sides of a channel. A skew bridge, which has a fixed direction (for instance North East), can be placed anywhere along the channel. Where to place it such that the path from A to B over the bridge is the shortest?
An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?
Two congruent right triangles on a common baseline have an overlap of variable size. What is the proportion of the minimal area to the maximal area?
A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
A square with two perpendicular lines. What is the minimal blue fraction?
A semicircle is inscribed in a rectangle. What is the minimal covered fraction?
A semicircle is inscribed in a quarter circle. What is the minimal yellow fraction?
A square contains a smaller square. Their vertices are cyclically connected as shown, forming four triangles. What is the minimal green area fraction?
You are standing in front of a mirror. Your shoulder width is 50 cm and your eyes are 6 cm apart. What is the minimum mirror width for a stereo view of yourself?