where
This formula is credited to Heron of Alexandria, although it is possible that it may have been known long before Heron's time.
The formula is in fact a special case of Brahmagupta's formula for the area of a cyclic quadrilateral; both of which are special cases of Bretschneider's formula[?] for the area of a quadrilateral.
Expressing Heron's formula with a determinant in terms of the squares of the distances between the three given vertices,
0 & a^2 & b^2 & 1 \\a^2 & 0 & c^2 & 1 \\ b^2 & c^2 & 0 & 1 \\
1 & 1 & 1 & 0\end{bmatrix} } </math>, illustrates its similarity to Tartaglia's formula for the volume of a foursimplex.
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