MathDB

Albatross and Frankinfueter both own a circle. Frankinfueter also has stolen from Prof. Trugweg a ruler. Before that, Trugweg had two points with a distance of

1

drawn his (infinitely large) board. For a natural number

n

, let A

(n)

be the number of the construction steps that Albatross needs at least to create two points with a distance of

n

to construct. Similarly, Frankinfueter needs at least

F(n)

steps for this. How big can

\frac{A (n)}{F (n)}

become? There are only the following three construction steps: a) Mark an intersection of two straight lines, two circles or a straight line with one circle. b) Pierce at a marked point

P

and draw a circle around

P

through one marked point . c) Draw a straight line through two marked points (this implies possession of a ruler ahead!).

Problem Statement