Lectures related to Spherical trigonometry

Surface Tension and Wetting: Solid/Liquid/Gas Interfaces

Explores surface tension, wetting, and the law of Laplace at interfaces.

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Introduction to Euclidean Geometry

Introduces the fundamental concepts of Euclidean geometry, exploring postulates, parallel lines, and non-Euclidean geometries.

Advanced Analysis II: Laplacian and Coordinates

Covers the Laplacian operator in different coordinate systems and its applications in differential equations.

Polar Coordinates: Position and Velocity

Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.

Stokes Formula: Streamfunction in Spherical Geometry

Explores vorticity equations, advection-diffusion, solid body rotation, and Stokes formula in spherical geometry.

Analytical Geometry: Proof of Exercise 5

Focuses on the proof of Exercise 5 in Analytical Geometry, emphasizing trigonometry concepts in solving geometric problems.

Local Frame: Navigation and Cartography

Explores local frames in navigation and cartography, emphasizing mathematical expressions and spatial relationships.

Trigonometric Circle Basics

Covers the trigonometric circle basics, including angles measurement and circular motion.

Reciprocal Trigonometric Functions

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Heat Conduction in Spherical Geometry

Analyzes heat conduction in non-planar geometry using a submarine example.

Lens Surfaces and Image Formation

Explains how to find the position and nature of images formed by lenses.

Learning Sparse Features: Overfitting in Neural Networks

Discusses how learning sparse features can lead to overfitting in neural networks despite empirical evidence of generalization.

Triple Integrals: Properties and Calculations

Covers the definition of triple integrals, properties, and calculation methods.

Introduction to Non-Euclidean Geometry

Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.

Power of a Point in Geometry

Explains measuring angles in trigonometric direction and determining angles at line intersections.

Geometric Constraints

Explores how to handle mechanical problems with geometric constraints and associated forces.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Triangle Relations: Cosine and Sine Laws

Explores the Cosine and Sine Laws in triangles, highlighting their applications and potential pitfalls.

Harmonic Oscillations: Superposition Principle

Explores harmonic oscillations and the superposition principle for solving trigonometric equations efficiently.