Is a 2000-Year-Old Formula Still Keeping Some Secrets?

For example, a = b = c = 1 defines an equilateral triangle and the formula gives Area = V3/4. However a = 3, b = c = 1 does not define a triangle, and the formula produces 4 45 This would have made perfect sense to the ancientsthere is no triangle, and there is no number. Today we know more: 4 1.677i is indeed a number, and that creates a problem. Does it mean that a = 3, b = c = 1 really does define some triangle? The formula tantalizes us: for example, a = 1.99, b = c = 1 just barely defines a triangle; the formula correspondingly gives a very small real area, which becomes zero as a increases to 2. As a increases beyond 2, the sides at first just miss forming a triangle, and the formula produces small imaginary numbers; as a increases, the sides get further and further away from forming a triangle, and the imaginary numbers grow. It seems that the formula is tracking triangles we don't see, and is reporting their areas to us. What's going on? After two millennia, is Heron's Formula still keeping some secrets?