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Geometric Constructions

Hi all,

I am going to start a new feed of problems related to geometric constructions through the usage of a straightedge and a collapsible compass. I will set some definitions here so that I will not have to constantly explain the terminology.

A straightedge is an arbitrarily long straight edge, without any markings. You can connect two points, draw a line through a point or draw an arbitrary line using it.

A collapsible compass is a circle drawing instrument which cannot be set to specific radii, but can draw a circle centred at a point passing through another, draw a circle centred at a point with an arbitrary radius or draw an arbitrary circle. However, it cannot copy a circle with the same radius after you draw one using it.

All constructions must be completely defined. E.g. if you are asked to draw an inscribed rhombus, you must draw any sides that aren't already defined. You cannot leave it as 4 points which satisfy being the vertices of a rhombus.

A move is defined as a use of either a straightedge or a collapsible compass. Marking in points doesn't count as a move.

A construction can be done in \(x\) moves if \(x\) is the minimum number of moves required to create it.

Good luck. :)

Note by Sharky Kesa
1 week ago

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