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Three points are collinear iff the determinant of the matrix of their barycentric coordinates vanishes

score 1.5k · Answer 1 · 2015-07-23 03:43:02

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Three points are collinear iff the determinant of the matrix of their barycentric coordinates vanishes

Published on 23 Jul 2015 - 3:43

score 762 · Answer 2 · 2015-10-24 00:54:30

762

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Three points of an affine space are collinear $\iff \det(A)=0$, with $A$ the matrix of the barycentric coordinates.

Published on 24 Oct 2015 - 0:54

score 2k · Answer 3 · 2015-10-25 12:29:24

2k

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Three lines are concurrent (or parallel) $\iff$ the determinant of its coordinates vanishes.

Published on 25 Oct 2015 - 12:29

score 1.8k · Answer 4 · 2026-03-20 15:11:19

1.8k

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Barycenter of a measure

Published on 20 Mar 2026 - 15:11

score 955 · Answer 5 · 2015-12-06 14:59:10

955

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Barycentric Coordinates in Equilateral Triangle

Published on 06 Dec 2015 - 14:59

score 114 · Answer 6 · 2016-02-16 21:58:14

114

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Number of 0-simplices after second barycentric subdivision of a standard simplex

Published on 16 Feb 2016 - 21:58

score 1.3k · Answer 7 · 2016-02-24 20:49:20

1.3k

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Determine if a point is inside a subtriangle by its barycentric coordinates

Published on 24 Feb 2016 - 20:49

score 308 · Answer 8 · 2016-06-29 20:48:30

308

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Barycentric coordinates

Published on 29 Jun 2016 - 20:48

score 134 · Answer 9 · 2026-03-24 02:47:50

134

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Baricenter of a region bounded by a closed parametric curve

Published on 24 Mar 2026 - 2:47

score 884 · Answer 10 · 2017-04-18 09:15:32

884

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How to make sense of the Barycentric coordinate system from Cartesian coordinate system?

Published on 18 Apr 2017 - 9:15

score 130 · Answer 11 · 2017-04-23 00:01:44

130

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Is there a generalized equation for a line in barycentric coordinates?

Published on 23 Apr 2017 - 0:01

score 443 · Answer 12 · 2017-06-22 20:43:30

443

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Barycentric Coordinates: How do I keep track of Ratios

Published on 22 Jun 2017 - 20:43

score 1k · Answer 13 · 2017-07-12 18:55:11

1k

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Is the integral of a linear function over a triangle always the average of the vertices?

Published on 12 Jul 2017 - 18:55

score 449 · Answer 14 · 2017-09-01 16:11:34

449

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formula for rational length cevians in an equilateral triangle

Published on 01 Sep 2017 - 16:11

score 1.8k · Answer 15 · 2017-10-03 09:08:39

1.8k

Views

Finding barycentric coordinates of a point $p$ in a triangle.

Published on 03 Oct 2017 - 9:08

List Question

Three points are collinear iff the determinant of the matrix of their barycentric coordinates vanishes

Three points of an affine space are collinear $\iff \det(A)=0$, with $A$ the matrix of the barycentric coordinates.

Three lines are concurrent (or parallel) $\iff$ the determinant of its coordinates vanishes.

Barycenter of a measure

Barycentric Coordinates in Equilateral Triangle

Number of 0-simplices after second barycentric subdivision of a standard simplex

Determine if a point is inside a subtriangle by its barycentric coordinates

Barycentric coordinates

Baricenter of a region bounded by a closed parametric curve

How to make sense of the Barycentric coordinate system from Cartesian coordinate system?

Is there a generalized equation for a line in barycentric coordinates?

Barycentric Coordinates: How do I keep track of Ratios

Is the integral of a linear function over a triangle always the average of the vertices?

formula for rational length cevians in an equilateral triangle

Finding barycentric coordinates of a point $p$ in a triangle.

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