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The ancients (the Greeks were most famous for this) were able to do a remarkable amount of mathematics through reasoning about these geometric figures.  [[Euclid]]'s book  ''The Elements'' is regarded as the best presentation of classical geometry.  The methods of reasoning described by Euclid are widely used even today to teach logical reasoning and the principles of axioms, theorems, and proofs.

The ancients (the Greeks were most famous for this) were able to do a remarkable amount of mathematics through reasoning about these geometric figures.  [[Euclid]]'s book  ''The Elements'' is regarded as the best presentation of classical geometry.  The methods of reasoning described by Euclid are widely used even today to teach logical reasoning and the principles of axioms, theorems, and proofs.

The mathematical "operations" that the ancient Greeks could do with these constructions include what we would now, in our number-centric world, would call addition,subtraction, multiplication, division, and square roots.  They could also solve problems of proportion, bisect arbitrary angles, find areas of a many shapes, and construct some, but not all, regular polygons.

The mathematical "operations" that the ancient Greeks could do with these constructions include what we would now, in our number-centric world, would call addition, subtraction, multiplication, division, and square roots.  They could also solve problems of proportion, bisect arbitrary angles, find areas of a many shapes, and construct some, but not all, regular polygons.

In modern times, compass-and-straightedge constructions were rediscovered by [[Euler]], who resurrected them from the pages of Euclid's ''Elements'' and found that their simple geometric [[truth]]s were a pleasant diversion from the [[calculus wars]] then raging between the {{hs|Isaac|Newton}}ian British and the [[Leibniz]]ian German mathematical communities. In the twentieth century, compass-and-straightedge methods have become a popular form of [[recreational mathematics]], and the technique is taught as a one-week [[unit]] in many [[middle school]] [[math]] [[class]]es.

In modern times, compass-and-straightedge constructions were rediscovered by [[Euler]], who resurrected them from the pages of Euclid's ''Elements'' and found that their simple geometric [[truth]]s were a pleasant diversion from the [[calculus wars]] then raging between the {{hs|Isaac|Newton}}ian British and the [[Leibniz]]ian German mathematical communities. In the twentieth century, compass-and-straightedge methods have become a popular form of [[recreational mathematics]], and the technique is taught as a one-week [[unit]] in many [[middle school]] [[math]] [[class]]es.