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Concepts8

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
⚙️AlgorithmIntermediate

Pick's Theorem

Pick's Theorem connects area and lattice-point counts for any simple polygon with integer-coordinate vertices.

#pick's theorem#lattice polygon#shoelace formula+12
⚙️AlgorithmIntermediate

Polygon Area and Centroid

The signed area of a simple polygon can be computed in O(n) using the shoelace formula, which sums cross products of consecutive vertices.

#shoelace formula
Advanced
Filtering by:
#cross product
#polygon area
#centroid
+12
⚙️AlgorithmIntermediate

Rotating Calipers

Rotating calipers is a geometric two-pointer technique that sweeps two (or more) parallel support lines around a convex polygon.

#rotating calipers#antipodal pairs#convex hull+12
⚙️AlgorithmIntermediate

Basic Geometry - Lines and Segments

A line can be represented by two points, a point with a direction vector, or the general form ax + by + c = 0, and these forms are interconvertible.

#line intersection#segment intersection#orientation test+12
⚙️AlgorithmIntermediate

Convex Hull

The convex hull is the smallest convex polygon that contains all given points, like a rubber band snapped around nails on a board.

#convex hull#graham scan#monotone chain+12
⚙️AlgorithmIntermediate

Point in Polygon

Point-in-polygon decides whether a point lies outside, inside, or on the boundary of a polygon.

#point in polygon#ray casting#winding number+11
⚙️AlgorithmIntermediate

Orientation and CCW

Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.

#orientation#ccw#cross product+12
⚙️AlgorithmIntermediate

Basic Geometry - Points and Vectors

A 2D point can be treated as a vector from the origin, so vector math (addition, scaling, dot, cross) applies directly to points.

#geometry#vector#dot product+11