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 F(n)A(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!). geometric constructionconstructiongeometry