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