I recently came across the so-called "Triangle Geometry" in which the area of an equilateral triangle with side length $1$ is fixed to be $1$. I was intrigued by the concept because of its simplicity and it led me to wonder how "Triangle Geometry" might apply to integration.
It certainly seems possible in 2 dimensions since an array of equilateral triangles tessellates 2D space. However, in practice, I haven't come up with any methods that are nearly as simple as the good ol' Riemann Integral.
Has anyone determined a more elegant way to integrate with "Triangle Geometry" or could point me to a resource that has?
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