Four-dimensional space

Formal sciences
Mathematics
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Euclidean geometry

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Geometric Projections: Understanding Monge's Method

Covers geometric projections using Monge's method, focusing on representing three-dimensional points through their orthogonal projections.

Turbulence: Scaling Exponents and Kolmogorov's Law

Delves into Kolmogorov's theory on turbulence, discussing scaling exponents and the 4/5-law.

Curse of Dimensionality in Deep Learning

Delves into the challenges of deep learning, exploring dimensionality, performance, and overfitting phenomena in neural networks.

Dimensional Analysis: Fundamentals and Applications

Covers dimensional analysis fundamentals and applications in scientific and engineering problems, including estimating atom size using Schrödinger's equation.

Rotation in Two Dimensions

Explores the equilibrium of forces and moments in a rotating system with a disc, mass, and counterweight.

Dimensional Analysis: Scaling and Theorems

Explores dimensional analysis, scaling, and the Buckingham theorem in analyzing physical systems.

Gravure Printing: Mechanisms and Effects

Covers the mechanisms and effects of gravure printing, including pattern formation, breakdown mechanisms, and substrate interactions.

Tensor Spaces and Unitary Representations

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Ordinary Differential Equations

Covers the extension of ordinary differential equations to n-dimensional space.

Rotation in Two Dimensions

Explores rotation in two dimensions, analyzing moment of inertia, acceleration, and stability using practical examples.