There is a square $ABCD$, line $EF$ and point $G$ on a plain. Can you construct the foot of perpendicular to line $EF$ through point $G$, using only a straightedge (in traditional Euclidean constructions)? Is there any construction shorter than mine?
I'd appreciate it if you posted a construction or provided any kinds of reference.
Here is my construction.
Complexity: 42
- Create a point $H$ on line $AC$.
- Create 2x2 grid:
ACBDI BHCDJ BCDHK AJBCL AKCDM ABHLN ADHMO CDINP BCIOQ - Create 2x4 grid:
ADNQR BCNOS BCOPT ADPQU NPRSV NPTUW - Create line $Id\bot EF$:
IOEFX ABVXY CDWXZ EFYZa ABIab AIObc ADNcd - Create rectangle $IhGl$:
GNIOe GPIOf NfPeg GgIOh GOINi GQINj OjQik GkINl - Create $Gp\bot EF$:
IGhlm GkIdn IOmno EFGop
- The complexity of a construction can be described by the quantity of points.
XYZUVis short for "creating point $V$ which is the intersection of line $XY$ and $ZU$".- Notice that points can be in either capital and lowercase letters.
