Lectures related to Epicyclic Curves: Modeling Instruments for Plane Curves

Explores homogeneous coordinates, curves, and unique solutions in Cartesian coordinates.

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Explores parametrized curves in 2D, including segments, straight lines, and circles with trigonometric functions.

Covers circle circumference calculation and parametric curve arc length determination.

Discusses tangents for circles and ellipses, poles, and duplication rule.

Explores the transition from geocentric to heliocentric models and the mathematical principles behind elliptical trajectories.

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.