Haversine formula

Q: How deeply does Optimization Algorithms: AI techniques for design, planning, and control problems cover haversine formula?

Defines the formula, intermediate quantities, Earth-radius parameter, and Python usage without developing its derivation.

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A trigonometric formula that computes spherical distance between two points from their latitude and longitude differences.

The haversine formula calculates the geographic distance between two points on Earth from their latitudes and longitudes, modeling Earth with a mean spherical radius. The result is also called great-circle distance. section 4.3.3

The calculation proceeds through these quantities:

Compute a = sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2). section 4.3.3
Compute C = 2 × atan2(√a, √(1 − a)). section 4.3.3
Multiply by the mean Earth radius: d = R × C, using 6,371 km or 3,691 miles. section 4.3.3

Los Angeles to Madrid

A Python implementation passes Los Angeles (34.052235, −118.243683) and Madrid (40.416775, −3.703790) to haversine(), then prints the resulting distance.

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

Cover of Optimization Algorithms: AI techniques for design, planning, and control problems

liveBook manning.com

Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

Related concepts

Euclidean distancealternative to · Euclidean distance is the straight-line distance between two points in Euclidean space, calculated as the square root of the sum of squared differences between corresponding coordinates.
distance matrixproduces · A distance matrix is a square array whose entries represent pairwise distances or dissimilarities between objects, points, or vertices.
similarity searchused by · Similarity search is a retrieval technique that finds or ranks items by comparing their representations with a query according to a similarity or distance measure.
riemannian distancekind of · Riemannian distance is the shortest distance between points on a curved space measured along that space rather than through its surrounding space.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.