UK Map Coverage with 1-Mile Radius Circles

This Marimo notebook calculates how many 1-mile radius circles are needed to cover the entire United Kingdom, saves the circle center points to a SQLite database, and visualizes them on an interactive map.

Features

• Fetches actual UK boundary data from GeoJSON sources
• Calculates optimal grid spacing using hexagonal-like packing (�3 × radius H 1.732 miles)
• Filters points to only include those within UK boundaries
• Stores all circle center coordinates (latitude/longitude) in SQLite database
• Visualizes coverage on an interactive Folium map
• Shows detailed statistics about coverage

Installation

1. Ensure you have Python 3.13+ and uv package manager installed
2. Install dependencies:

uv sync

Usage

Run the Marimo notebook:

uv run marimo edit main.py

This will open the notebook in your browser where you can:

• See the step-by-step calculation process
• View the total number of circles needed
• Explore the interactive map visualization
• Access the database with all circle centers

Database

The circle center points are saved to uk_coverage.db with the following schema:

CREATE TABLE circle_centers (
    id INTEGER PRIMARY KEY AUTOINCREMENT,
    latitude REAL NOT NULL,
    longitude REAL NOT NULL,
    created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
)

Query the Database

You can query the database using Python:

import sqlite3

conn = sqlite3.connect('uk_coverage.db')
cursor = conn.cursor()

# Get all circle centers
cursor.execute("SELECT latitude, longitude FROM circle_centers")
points = cursor.fetchall()

print(f"Total circles: {len(points)}")
conn.close()

How It Works

1. UK Boundary: Fetches actual UK administrative boundaries from GeoJSON data
2. Grid Generation: Creates a hexagonal-like grid with 1.732-mile spacing between centers
3. Filtering: Only keeps points that fall within UK boundaries
4. Database Storage: Saves all valid circle centers to SQLite
5. Visualization: Displays a sample of circles on an interactive map (showing 500 circles to avoid performance issues)

Adjusting Parameters

To change the circle radius or coverage area, modify these variables in main.py:

• radius_miles: Change the circle radius (line 81)
• spacing_miles: Adjust grid spacing for different coverage patterns (line 82)
• UK boundary URL can be changed in the get_uk_boundary() function (line 43)

Technical Details

• Uses hexagonal-like packing with spacing = radius × �3 for optimal coverage
• Coordinates are in WGS84 (EPSG:4326) decimal degrees
• Distance calculations account for Earth's curvature at UK latitude (~55°N)
• Map visualization samples 500 circles for performance (all points are in database)