• Cyclic quadrilaterals
• Projective geometry
• Taxicab Geometry
• Heron's Theorem
• Ceva's Theorem
• Gergonnne Point
• The Brocard Circle and Brocard Point
• Orthogonal Circles
• Menelaus' Theorem
• The Fermat Point
• Reuleaux Triangle
• Napolean's Theorem
• Simson's Theorem
• Locus of centers of circles passing through two points, or tangent to a line m at point T, or tangent to a circle at point T, or with radius r and tangent to line m, OR tangent to two lines m and n intersecting at O
• Star polygons
• Kaleidoscopes
• Penrose Tessellations
• Construction of Pythagorean Triplets
• Constructible Numbers
• Constructible Polygons
• Golden Rectangle and its related Spiral
• Platonic and Archimedean Polyhedra, or Stellations, or Non-Convex Uniform Polyhedra
• Regular Spherical Models (such as a spherical octahedron), or semi-regular spherical models, or any category of the variations
• Birkoff's Axioms for Geometry
• Hilbert's Axioms for Geometry
• Klein-Beltrami Model for non-Euclidean Geometry
• A self-dual Finite Geometry
• Sphere Packing Problem
• Three Famous Greek Construction Problems - Trisection of an Angle, Doubling a cube, or Squaring the Circle
• Mascheroni Constructions
• Transformations using Matrices
• Transformations in 3-Space with Invariant Points
• Geometry of Fractals and their dimensions
• Problem of Appolonius
• Power of a Point with respect to a Circle
• Tomahawk Method for Trisecting an angle (can be done in Sketchpad)
• Coordinate Geometry