How can I construct such Golden Ratio Gauge?
What shall be the lengths of respective legs (their parts)?
$M, P, N$ - are sharpened tips (endpoints)
$A, B, C, D$ - joints (screw-points)
2026-03-25 18:59:07.1774465147
How can I construct a Golden Ratio Gauge like this? What shall be the legs of such a gauge?
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If $\overline{AB}$, $\overline{AC}$, $\overline{BD}$, $\overline{CD}$ are all one unit long, then $\overline{BM}$, $\overline{BP}$, $\overline{CN}$ need to be $\phi$ units long.
You can see this by drawing a line through $P$ parallel to $\overline{CD}$. Let's say this line intersects $\overline{AN}$ at $Z$. Then the parallelogram $AZPB$ is the usual golden rectangle, skewed into a parallelogram. Triangles $\triangle MBP$ and $\triangle PZN$ are similar with side-length ratios $\phi$.