Symmedian -- smuckedian. There's no practical differences among any of these triangle "centers" that have been discussed. The symmedian is the MPP from logical inference, which is based on incomplete knowledge. Or should we rephrase that last part, saying it's based on ignorance.
The attached plot, having a relatively large cocked hat, shows that the 0.53%/area value at the MPP is negligibly greater than any reasonable point inside the hat, which would certainly be less than 0.45%/area. That 0.08% difference is irrelevant for practical navigation.
(Dividing the
distance scale by 10 and calling these units minutes of arc, scales sigma to 7.5' and the side farthest from the MPP to 3 nm from the MPP.)
Maybe just remembering that the symmedian is closest to the shortest hat side, and next closest to the next shortest side is all that's needed in eyeballing. I think this agrees with Herbert.
John K
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