A333944 Constructibility sequence, the number of points constructed by straightedge and compass after successive stages of forming all possible lines, circles, and intersection points, beginning with 2 points.

2, 6, 203, 1723816861

Offset

1,1

Comments

The fourth value was computed by Teofil Camarasu, taking 6 days of computer time performing exact algebraic computations (see link to Mathematics Stack Exchange).

Note that circles are formed only by specifying an already existing segment as radius (so we have collapsible compasses only).

References

Joel David Hamkins, Lectures on the Philosophy of Mathematics, MIT Press, 2020, chapter 4. (in press)

Links

Table of n, a(n) for n=1..4.

Joel David Hamkins, Mathematics Stack Exchange question, What is the next number on the constructibility sequence? And what is the asymptotic growth?, including answers by Teofil Camarasu and Pace Nielsen.

Joel David Hamkins, Illustrating the construction sequence: Begin with 2 points, stage 1, 6 points at stage 2, 203 points at stage 3.

Example

Begin with 2 points A and B. Construct the line containing them and the two circles having AB as radius; these intersect at four additional points, making 6 points in all. Using these 6 points, one may construct 9 new lines and 14 new circles, leading to 203 intersection points in all.

Crossrefs

Sequence in context: A345726 A302344 A156517 * A091439 A285102 A285101

Adjacent sequences: A333941 A333942 A333943 * A333945 A333946 A333947

Keyword

nonn,hard,more

Author

Joel David Hamkins, Apr 11 2020

Status

approved