https://en.wikipedia.org/wiki/Simplex
replyCommon for visualizing mixtures of three things!
While you are technically correct, since any triangle is a simplex, this is not relevant to this visualization.
replyFor this visualization: get positive quantities in 3D space, normalize to 1, now you have dot on a triangle on 1-sphere in a positive octant. Project triangle into 2D space a this is your visualization.
2-sphere, I believe you mean to say.
replyIt's easy, if you normalize it so that it sums to one, it drops a dimension, and becomes an equilateral triangle.
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