Lectures related to Geometric Modeling for Architects: Ellipses and Structures

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Conics in the Plane: Uniform Description of 3 Conics

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

Ellipses in Astronomy and Mathematics: Key Concepts

Covers the properties and applications of ellipses in astronomy and mathematics, including Kepler's laws and practical construction methods.

Geometric Properties of Conics: Ellipses and Their Applications

Covers the geometric properties of ellipses, their definitions, and applications in mathematics and astronomy.

Geometric Properties of Ellipses and Their Applications

Explores the geometric properties of ellipses, their parametric equations, and applications in architecture and design.

Introduction to Conic Sections in Space

Covers the introduction to conic sections in space, focusing on ellipses and their properties.

Concatenation of Arcs in Geometry

Delves into the historical and geometric aspects of arc concatenation, including ellipse approximation and architectural applications.

Ellipse: Astronomical Evolution to Mathematical Formulation

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

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Conics in Geometry: Ellipses, Parabolas, and Hyperbolas

Provides an overview of conics, including ellipses, parabolas, and hyperbolas, focusing on their properties, equations, and applications in geometry and physics.

Gothic Surfaces: Curvature, Development, and Stereotomy

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

Geometric Analysis: Singularities in Architectural Design

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Conic Sections: Equivalence and Intersection

Delves into the historical context and mathematical properties of conic sections like parabolas, ellipses, and hyperbolas.

Geometry: Instrument Epicycle

Explores the invention of instruments by artists like Albrecht Dürer to draw complex curves and lines not achievable with a ruler.

Dandelin Theorem: Ellipse Construction

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Conic Sections: Ellipse, Parabola, Hyperbola

Explores conic sections like ellipse, parabola, and hyperbola, their properties, constructions, and perspectives in 2D and 3D spaces.

Hyperboloid Surfaces: Sections and Developability

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Conic Sections: Definitions and Equations

Explores the definitions and equations of conic sections, including parabolas, ellipses, and hyperbolas, with practical geometric applications.

Inequality of Seasons: Earth's Orbit Representation

Explores the inequality of seasons by examining the Earth's orbit and the causes of the seasons in architecture and gnomonics.

Elliptical Curves: Construction and Variants

Explores the construction and variants of elliptical curves, including historical stonecutting methods and architectural considerations.