I have a problem. I have a triangle grid with a lot of equilateral triangles. Now I want to know what the distance is between two centroids. How can I do that?
Here is a sample image of the grid:triangle grid
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1Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos May 22 '19 at 07:43
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Supposing the grid length is 1 unit, we know the distance from the centroid to a side is $\frac{1}{2\sqrt{3}}$ units. Thus the distance between two neighbouring centroids is $\frac{1}{\sqrt{3}}$. For centroids that are further apart, note that the centroids form a hexagonal grid; computation from here is not too difficult.
auscrypt
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It is easy to decompose the grid into triangles and show that the equilateral triangles which make up the hexagons have a third of the area of the original triangles. And that gives an easy computation of the distance. – Mark Bennet May 22 '19 at 07:41
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Can you work out the perpendicular height of your triangles?
The distance from the base of a triangle to its centroid if $h \over 3$, where $h$ is the perpendicular height of the triangle.
The distance between two centroids is then this distance doubled.
tomi
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