Helical Curves: Theory and Applications

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Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Geometric Analysis: Singularities in Architectural Design

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

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Mechanics of Kirchhoff Rods: Finite Strain and Rotation Theory

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Nonlinear Beam Theory: Mechanics of Slender Structure

Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.

Symmetry in Modern Geometry

Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.

Surfaces with Constant Curvature

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.