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I don't think it matters to Rand's theory what quantities are directly measurable or not. Side-length is a measurement, average of side-lengths is a measurement, angles are measurements, sines and tangents of angles are measurements. These are all characteristics of a triangle, even if we might need to perform some computations to find them out. It's possible to restate your definition in terms of quantities that are "directly measurable": we just need the ratio of a triangle's side-length to its perimeter (which is "directly measurable") to be between 0.9/3 and 1.1/3. However, even here we need to "compute" the ratio (which isn't directly measurable). The measurement omission here is the fact that only the ratios matter, not the actual lengths. This isn't actually necessary. It was just the easiest way. Since we know for a fact that only the ratios matter, we can discard all length measurements as a first step (and instead just look at angles). Thus, even without computing averages, we can omit all length measurements (since they're just indicators of scale). Then, based on the law of sines, we can apply the following conditions: 0.9/3 < sin(A)/(sin(A)+sin(B)+sin(B)) < 1.1/3 0.9/3 < sin(B)/(sin(A)+sin(B)+sin(B)) < 1.1/3 0.9/3 < sin(C)/(sin(A)+sin(B)+sin(B)) < 1.1/3 Even after this, there are additional measurement omissions (only ratios of sines matter, not the actual values of the sines. The exact value of the ratio also doesn't matter and only a certain range matters). The idea that we need to compute averages before any measurement omission is incorrect. It's possible to get rid of length measurements first and then do other computations. However, calculating averages first is easier (and it honestly doesn't matter. The average is as much a property of a triangle as a side-length).