Geometry
Shapes, sizes, and the relationships between them. From the foundational ideas of point, line, and plane, geometry builds up to the rigorous proof culture that taught the world how to argue — and gives us the language of space.
Points, Lines & Planes
The undefined building blocks of geometry. Postulates, axioms, and how rigorous proof starts.
Angles
Measuring rotation between two rays. Acute, right, obtuse, straight, and the relationships between angles that cross or share a vertex.
Triangles
The simplest polygon. Classification by sides and angles, the angle-sum theorem, and the rules of congruence.
The Pythagorean Theorem
a² + b² = c² — the most famous theorem in elementary math, with a dozen proofs and a thousand applications.
Polygons & Quadrilaterals
Closed plane figures with three or more straight sides. Squares, rectangles, parallelograms, trapezoids, and the family relationships.
Area & Perimeter
How much space a shape covers and how much fence you'd need around it. Formulas for the basic shapes and how they're derived.
Circles
The set of points equidistant from a center. Radius, diameter, circumference, area, and the role of π.
Coordinate Geometry
Descartes' bridge between geometry and algebra. Distance and midpoint, slope, line and circle equations on the Cartesian plane.
Transformations
Translation, rotation, reflection, dilation. Isometry vs similarity, coordinate rules, and symmetry as invariance.
Tessellations
Tiling the plane with no gaps or overlaps. Regular, semi-regular, Escher-style modifications, and the deep symmetry of the 17 wallpaper groups.
Conic Sections
The four curves you get by slicing a double cone — circle, ellipse, parabola, hyperbola — unified by focus, directrix, and eccentricity.
Three-Dimensional Solids
Prisms, pyramids, cylinders, cones, spheres. The five Platonic solids, Euler's V − E + F = 2, nets, and cross-sections.
Surface Area & Volume
Stepping up to 3D. Prisms, pyramids, cylinders, cones, and spheres — what's their skin and what's inside.