Exploring Classical Greek Construction Problems with Interactive Geometry Software
In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves.
By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.
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7Sect ABCD Adriaan van Roomen Aguilon Apollonius Archimedean spiral Archimedes area circular C1 and C2 calculate Cartesian equation Ceulen circle centered circle with radius circular sector circumscribed compass and straightedge compass point conchoid conic sections constructible numbers cosÂ Create an IGS cube curve Define a slider Determine the intersection diameter directrix Draw a circle Draw the straight drawing by Paul edge equal Euclid figure François Viète given Gregory’s heptagon Hippocrates hyperbola IGS file inscribed Interactive Geometry Software intersection points intersects the circle kABk kCDk kDBk kOBk line segment line segment ŒAB lunes mathematician Meskens midpoint neusis Nicomedes ŒAC parabola parallel Paul Tytgat perpendicular bisector Plato’s polar equation polygon postulate procedure proof Prove Pythagoras quadratrix rectangle right-angled triangle Roomen semi-circle sinÂ sino slider solve squarable straight line straightedge construction straightedge methods tangent circle theorem triangle 4ABC trisect an angle trisectrix vertex Viète x-axis