Dynamic projective geometry

摘要: The theme of this thesis is dynamic geometry, a new way exploring classical geometry using interactive computer software. This kind software allows the user to make geometric constructions on computer's screen. might consist points, lines and conics whose positions have been constrained in various ways. constraints, which may involve incidences, distances angles, can be added removed dynamically. For example, force line always incident point, would simply grab with cursor drop it onto point. Any object position not completely determined by constraints grabbed dragged around rest objects will then automatically self-adjust order keep satis ed. Dynamic primarily used for teaching mathematics, but useful any situation where important understand properties system. Over last few years, number tools developed. Most them focused elementary Euclidean geometry. In we present that has based entirely projective concepts thus us illustrate theorems also extensive support di erent types metrics, makes possible explore both non-Euclidean fact, given direct access absolute elements de ne metric. Moreover, system handle complex plane, permits, circular points constructions. We discuss how interface should designed identify problems shortcomings interfaces all previous systems seem su er from. these defects are related fundamental problem choosing right solution an underdetermined constraint equations. show solved letting add extra if necessary, richer internal representation oriented written English.