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mc776Two points, M and F, are placed along the X axis.
A third point, G, is arbitrarily placed. The resulting triangle almost never has a right or obtuse angle, except in rare cases the corner occupied by G itself.
This setup is filtered through a representation that only shows points along the X axis, discarding all other data.
For any unequal length of GM and GF, given any non-zero value for G.y:
Example:
M at (-5,0)
F at (5,0)
G at (1,5)
abs(G.x-M.x)= 6
abs(G.x-F.x)= 4
proportion 1.5
6*6+25=36+25= 61
4*4+25=16+25= 41
GM~= 7.8
GF~= 6.4
proportion 1.219
One consequence is that, for any given G, the relative difference between GM and GF is always going to be exaggerated when viewed through the flattened representation. Where G.y is much greater than MF, GM and GF may be different by a rounding error while the flat representation shows an enormous bias one way or the other.
A third point, G, is arbitrarily placed. The resulting triangle almost never has a right or obtuse angle, except in rare cases the corner occupied by G itself.
This setup is filtered through a representation that only shows points along the X axis, discarding all other data.
For any unequal length of GM and GF, given any non-zero value for G.y:
- GM will be longer than the distance from G.x to M.x.
- GF will be longer than the distance from G.x to F.x.
- The proportion between GM and GF will be closer to 1 than will the proportion of the distance from G.x to M.x versus G.x to F.x.
Example:
M at (-5,0)
F at (5,0)
G at (1,5)
abs(G.x-M.x)= 6
abs(G.x-F.x)= 4
proportion 1.5
6*6+25=36+25= 61
4*4+25=16+25= 41
GM~= 7.8
GF~= 6.4
proportion 1.219
One consequence is that, for any given G, the relative difference between GM and GF is always going to be exaggerated when viewed through the flattened representation. Where G.y is much greater than MF, GM and GF may be different by a rounding error while the flat representation shows an enormous bias one way or the other.