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Geometry and Analysis

Geometry

• Six types of Ruled Surfaces
• Half Twist Ruled Surfaces
• p/q Twist Ruled Surfaces
• Saddle (hypar) Surfaces
• The Seven Wonders of the Ancient World


The 13 Archimedian semiregular polyhedra

Theorems

• The Mathematician's Quest for Superlatives . . .from geometrical and caculus considerations
• The Mathematician's Quest for Superlatives . . .using caculus of variations
• Certain Periodic Polar Curves
• Monge's Twist-surface Theorems
• Hyperpower Function _xx^{x . . .}
• Theorems of Girolamo Sacceri, S.J. and his hyperbolic geometry
• Saccheri's Solution to Euclid's BLEMISH

Course syllabi

Double helicoid in a cylinder	Focal lines in a cylinder