D12913: Golden ratio point
noreply at phabricator.kde.org
Wed May 16 13:04:55 UTC 2018
paolini added a comment.
I have one remark. Since the result is different depending on how we orient the segment (say) AB we have to decide if the construction
gives the point on the segment nearest to A or the one nearest to B. The proposed solution:
a + (3 - sqrt(5)) * (b - a) / 2
gives the point nearest to A, whereas it seems to me more natural to construct the point nearest to B:
a + (sqrt(5) - 1) * (b - a) / 2
This seems to be closer to the usual definition as that portion of AB that is "mean proportional" between the whole segment and the remaining part, which I would interpret as: find C in AB such as |AB| : |AC| = |AC| : |CB| (i.e. we construct the golden section starting from A, not from B).
Cc: paolini, kde-edu, narvaez, apol
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