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please do so. If it no longer meets these criteria, you can
reassess it. Review: April 20, 2022. ( Reviewed version). |
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Might be true (in some sense, asymptotically) but I no longer find this at all evident. Another way to pose the question: for P, Q points from the configuration X, the line segment PG having length L, we want to draw strips of width inversely proportional to L and look whether any other point R lies in them (because the area of the triangle PQR is L times the perpendicular distance from R to the line).
Charles Matthews 09:35, 25 Sep 2004 (UTC)
Hi there, I'm pleased to inform you that I've begun reviewing the article "Heilbronn triangle problem" you nominated for
GA-status according to the
criteria. This process may take up to 7 days. Feel free to contact me with any questions or comments you might have during this period.
Eluike (
talk) 19:43, 8 April 2022 (UTC)
GA toolbox |
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Reviewing |
Reviewer: Ovinus ( talk · contribs) 14:55, 19 April 2022 (UTC)
I'll take another one. Ovinus ( talk) 14:55, 19 April 2022 (UTC)
Looks good overall. Understandable for most undergraduate CS students, I'd say. Ovinus ( talk) 14:55, 19 April 2022 (UTC)
Some readers might find the article more appealing if it included "eye candy" in the form of some optimal solutions for n around 10. There's plenty of material at https://mathworld.wolfram.com/HeilbronnTriangleProblem.html. The images there are copyright, but I don't believe the coordinates are, so making SVGs should not be hard. Maproom ( talk) 07:36, 20 April 2022 (UTC)
boring data
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$n = 7; my $z = 0.287258; $p[0] = [ -$z*50/19-$z*$z*17/38 +37/38, 0 ]; $p[1] = [ 1, 0 ]; $p[2] = [ 0, $z ]; $p[3] = [ 9/19+$z*$z/19+$z*7/19, $z ]; $p[4] = [ $z*$z*40/19 +$z*223/19-58/19, -1 +6*$z +$z*$z ]; $p[5] = [ $z*58/19-15/19 +$z*$z*11/19, 1 ]; $p[6] = [ 1, 1 ]; $n = 8; my $p = sqrt(13); $p[0] = [ 0, 0 ]; $p[1] = [ (1+$p)/6, 0 ]; $p[2] = [ 1, (7-$p)/18 ]; $p[3] = [ (5-$p)/6, (7-$p)/9 ]; $p[4] = [ (1+$p)/6, (2+$p)/9 ]; $p[5] = [ 0, (11+$p)/18 ]; $p[6] = [ (5-$p)/6, 1 ]; $p[7] = [ 1, 1 ]; $n = 9; $p = sqrt(65); $p[0] = [ (10-$p)/10, 0 ]; $p[1] = [ (25+$p)/40, 0 ]; $p[2] = [ 0, (15-$p)/40 ]; $p[3] = [ 1, (15-$p)/40 ]; $p[4] = [ (15-$p)/20, (5+$p)/20 ]; $p[5] = [ 0, (35+3*$p)/80 ]; $p[6] = [ 1, $p/10 ]; $p[7] = [ (45-3*$p)/80, 1 ]; $p[8] = [ (25+$p)/40, 1 ]; $n = 10; my $x = 0.157806; my $y = 0.252387; $z = 0.315611; $p[0] = [ $x, 0 ]; $p[1] = [ 1-$y, 0 ]; $p[2] = [ 0, $x ]; $p[3] = [ 1, $y ]; $p[4] = [ 1-$z, $z ]; $p[5] = [ $z, 1-$z ]; $p[6] = [ 0, 1-$y ]; $p[7] = [ 1, 1-$x ]; $p[8] = [ $y, 1 ]; $p[9] = [ 1-$x, 1 ]; $n = 11; $p[0] = [ 1/3, 0 ]; $p[1] = [ 2/3, 0 ]; $p[2] = [ 0, 2/9 ]; $p[3] = [ 1, 2/9 ]; $p[4] = [ 1/3, 4/9 ]; $p[5] = [ 2/3, 4/9 ]; $p[6] = [ 0, 2/3 ]; $p[7] = [ 1, 2/3 ]; $p[8] = [ 1/2, 7/9 ]; $p[9] = [ 1/6, 1 ]; $p[10] = [ 5/6, 1 ]; $n = 12; $x = 0.115354; $y = 0.180552; $p[0] = [ $x, 0 ]; $p[1] = [ 1-$x, 0 ]; $p[2] = [ 0, $x ]; $p[3] = [ 1, $x ]; $p[4] = [ 1/2, $y ]; $p[5] = [ $y, 1/2 ]; $p[6] = [ 1-$y, 1/2 ]; $p[7] = [ 1/2, 1-$y ]; $p[8] = [ 0, 1-$x ]; $p[9] = [ 1, 1-$x ]; $p[10] = [ $x, 1 ]; $p[11] = [ 1-$x, 1 ]; |
The replacement with gray edges looks a little light to me — either the points or the lines need to be stronger, to see it more clearly. I thought the black edge versions were ok. — David Eppstein ( talk) 20:33, 5 May 2022 (UTC)
I'm making this a new section rather than appending it to the one above. I consider most of the stuff discussed in the above section as resolved, though I'm open to suggestions for changes in the diagrams. But there's one aspect which still worries me.
When Ovinus suggested "highlight a single one of the minimal area triangles", my views followed this trajectory:
I'm not going to do anything about this for a while. Maybe my thoughts will be different in a few days. Maybe someone will offer some good advice.
I've long stopped pretending to myself that I'm avoiding WP:OR. Maybe WP:OR doesn't apply to diagrams? If I add a picture of a dandelion to Taraxacum, no-one complains about WP:OR. Maproom ( talk) 19:35, 8 May 2022 (UTC)
![]() | Heilbronn triangle problem has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: April 20, 2022. ( Reviewed version). |
![]() | This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Might be true (in some sense, asymptotically) but I no longer find this at all evident. Another way to pose the question: for P, Q points from the configuration X, the line segment PG having length L, we want to draw strips of width inversely proportional to L and look whether any other point R lies in them (because the area of the triangle PQR is L times the perpendicular distance from R to the line).
Charles Matthews 09:35, 25 Sep 2004 (UTC)
Hi there, I'm pleased to inform you that I've begun reviewing the article "Heilbronn triangle problem" you nominated for
GA-status according to the
criteria. This process may take up to 7 days. Feel free to contact me with any questions or comments you might have during this period.
Eluike (
talk) 19:43, 8 April 2022 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: Ovinus ( talk · contribs) 14:55, 19 April 2022 (UTC)
I'll take another one. Ovinus ( talk) 14:55, 19 April 2022 (UTC)
Looks good overall. Understandable for most undergraduate CS students, I'd say. Ovinus ( talk) 14:55, 19 April 2022 (UTC)
Some readers might find the article more appealing if it included "eye candy" in the form of some optimal solutions for n around 10. There's plenty of material at https://mathworld.wolfram.com/HeilbronnTriangleProblem.html. The images there are copyright, but I don't believe the coordinates are, so making SVGs should not be hard. Maproom ( talk) 07:36, 20 April 2022 (UTC)
boring data
|
---|
$n = 7; my $z = 0.287258; $p[0] = [ -$z*50/19-$z*$z*17/38 +37/38, 0 ]; $p[1] = [ 1, 0 ]; $p[2] = [ 0, $z ]; $p[3] = [ 9/19+$z*$z/19+$z*7/19, $z ]; $p[4] = [ $z*$z*40/19 +$z*223/19-58/19, -1 +6*$z +$z*$z ]; $p[5] = [ $z*58/19-15/19 +$z*$z*11/19, 1 ]; $p[6] = [ 1, 1 ]; $n = 8; my $p = sqrt(13); $p[0] = [ 0, 0 ]; $p[1] = [ (1+$p)/6, 0 ]; $p[2] = [ 1, (7-$p)/18 ]; $p[3] = [ (5-$p)/6, (7-$p)/9 ]; $p[4] = [ (1+$p)/6, (2+$p)/9 ]; $p[5] = [ 0, (11+$p)/18 ]; $p[6] = [ (5-$p)/6, 1 ]; $p[7] = [ 1, 1 ]; $n = 9; $p = sqrt(65); $p[0] = [ (10-$p)/10, 0 ]; $p[1] = [ (25+$p)/40, 0 ]; $p[2] = [ 0, (15-$p)/40 ]; $p[3] = [ 1, (15-$p)/40 ]; $p[4] = [ (15-$p)/20, (5+$p)/20 ]; $p[5] = [ 0, (35+3*$p)/80 ]; $p[6] = [ 1, $p/10 ]; $p[7] = [ (45-3*$p)/80, 1 ]; $p[8] = [ (25+$p)/40, 1 ]; $n = 10; my $x = 0.157806; my $y = 0.252387; $z = 0.315611; $p[0] = [ $x, 0 ]; $p[1] = [ 1-$y, 0 ]; $p[2] = [ 0, $x ]; $p[3] = [ 1, $y ]; $p[4] = [ 1-$z, $z ]; $p[5] = [ $z, 1-$z ]; $p[6] = [ 0, 1-$y ]; $p[7] = [ 1, 1-$x ]; $p[8] = [ $y, 1 ]; $p[9] = [ 1-$x, 1 ]; $n = 11; $p[0] = [ 1/3, 0 ]; $p[1] = [ 2/3, 0 ]; $p[2] = [ 0, 2/9 ]; $p[3] = [ 1, 2/9 ]; $p[4] = [ 1/3, 4/9 ]; $p[5] = [ 2/3, 4/9 ]; $p[6] = [ 0, 2/3 ]; $p[7] = [ 1, 2/3 ]; $p[8] = [ 1/2, 7/9 ]; $p[9] = [ 1/6, 1 ]; $p[10] = [ 5/6, 1 ]; $n = 12; $x = 0.115354; $y = 0.180552; $p[0] = [ $x, 0 ]; $p[1] = [ 1-$x, 0 ]; $p[2] = [ 0, $x ]; $p[3] = [ 1, $x ]; $p[4] = [ 1/2, $y ]; $p[5] = [ $y, 1/2 ]; $p[6] = [ 1-$y, 1/2 ]; $p[7] = [ 1/2, 1-$y ]; $p[8] = [ 0, 1-$x ]; $p[9] = [ 1, 1-$x ]; $p[10] = [ $x, 1 ]; $p[11] = [ 1-$x, 1 ]; |
The replacement with gray edges looks a little light to me — either the points or the lines need to be stronger, to see it more clearly. I thought the black edge versions were ok. — David Eppstein ( talk) 20:33, 5 May 2022 (UTC)
I'm making this a new section rather than appending it to the one above. I consider most of the stuff discussed in the above section as resolved, though I'm open to suggestions for changes in the diagrams. But there's one aspect which still worries me.
When Ovinus suggested "highlight a single one of the minimal area triangles", my views followed this trajectory:
I'm not going to do anything about this for a while. Maybe my thoughts will be different in a few days. Maybe someone will offer some good advice.
I've long stopped pretending to myself that I'm avoiding WP:OR. Maybe WP:OR doesn't apply to diagrams? If I add a picture of a dandelion to Taraxacum, no-one complains about WP:OR. Maproom ( talk) 19:35, 8 May 2022 (UTC)