Seven Lines Not Sufficient For Poncelet-Steiner

Beginning with Martin's four points, we have seen a trisecting construction using eight lines. 

The proof that seven lines is not enough is contained in this Maple file.  In fact, this file generates all line-only constructions up to ten lines.  A list of all points that can be constructed by two through ten lines is given in this Maple file. 

We summarize by giving the number of points generated by N lines with Martin's starting configuration. 

We begin with Martin's four points (1,0), (2,0), (0,1) and (0,2).   If we use N lines, we have M possible new points where

N= 2 lines:   M = 2 new points

N= 3, 4, 5 lines:  no additional points

N= 6 lines:   M = 2

N = 7:   M = 6

N= 8:   M = 11

N= 9:   M = 70

N = 10:   M = 309

Return to Eight Line Construction Page

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