Since this is a math question area, I'm going to answer mathematically:
make your points (-1,1), (0,1), (1,0), (-1,0), (0,0), (1,0), (-1,-1), (0,-1), (1,-1).
Define f:R-->R^2 by the following piecewise parametric equations.
Start at point (-1,-1) and draw a line to (1,1) This is given parametrically by (x,y)=(t-1,t-1) where 0â¤tâ¤2.
Now draw a line to (1,-2). This is given parametrically by (x,y)=(1,3-t) where 2â¤tâ¤5.
Now draw a line to (-2,1), this is given by (x,y)=(6-t,t-7) where 5â¤tâ¤8.
Finally draw a line to (0,1), this is given by (x,y)=(t-10,1) where 8â¤tâ¤10.
To see that it is continuous, you must compare the two meeting functions at the points where they intersect (2,5,8):
f(2)=(2-1,2-1)=(1,1)
=(1,3-2)=(1,1) so t=2 is OK.
f(5)=(1,3-5)=(1,-2)
=(6-5,5-7)=(1,-2) so t=5 is OK
f(8)=(6-8,8-7)=(-2,1)
=(8-10,1=(-2,1) so t=8 is OK
Thus f is continuous (meaning, you didn't have to pick up the pen).
To see that it passes through every point:
f(0)=(-1,-1)
f(1)=(0,0)
f(2)=(1,1)
f(3)=(1,0)
f(4)=(1,-1)
f(6)=(0,-1)
f(7)=(-1,0)
f(9)=(-1,1)
f(10)=(0,1)
Thus it passes through every point.
here is a link of it flipped horizontally: http://www.puzzles.com/PuzzlePlayground/NinePoints/NinePointsSol.htm
2006-07-11 15:42:21
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answer #2
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answered by Eulercrosser 4
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you can, but lines have to go outside of the "sqaure" formed by the dots.
Start from bottom left dot,
1st line goes to top-right dot
2nd line goes down through bottom-right dot, and one more space down
3d line goes up-left through two dots and ends one space left of top-left dot
4th line goes right to top-right dot.
2006-07-11 15:34:35
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answer #3
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answered by Anonymous
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