Curvature

About

Curvature is a geometry and visibility toolkit for anyone who wants to test what a curved or flat Earth would predict, with every formula documented and every assumption stated. THE CALCULATOR Enter observer height, target height and surface distance. Curvature returns the surface horizon, tangent-plane drop, midpoint bulge, horizon dip, surface tilt and the hidden and visible portions of the target, in metres or feet, kilometres or miles. Choose refraction off, four published coefficients or your own k from 0 to 0.5, and compare any result side by side with the pure geometric case. Drag the observer, target and distance directly on an exaggerated profile, or switch to a true-scale view with a magnified detail inset. Uncertainty ranges recalculate across your stated input tolerances so you can see whether a sighting is robust. THE MAP Drop rulers and points of interest on standard, satellite or hybrid maps. Rulers report geodesic surface distance and initial bearing in degrees or NATO mils, search for places, fit the view and send endpoints straight to the calculator. Optional terrain lookup prefills ground elevations from SRTM data with the datum and limits spelled out. THE 3D MODEL EXPLORER (NEW) Explore three scenarios with the same observer, date and time: the classical north-polar disc, a south-polar projection comparison and a WGS84 reference ellipsoid. The globe uses dated geometric ephemerides from the open-source Astronomy Engine, including sidereal rotation, precession, nutation, seasons, real Earth-Sun and Earth-Moon distances and lunar illumination, validated against JPL Horizons and US Naval Observatory data. Place the observer anywhere, read elevation, bearing, slant distance and angular diameter for the Sun and Moon, then open the observer sky to see both at their calculated angular size. A comparison sheet lists all three models for the same inputs. Each scene labels what is sourced, what is an app assumption and what is not simulated. REPORTS AND ANALYSIS Export an illustrated PDF report with inputs, coordinates, assumptions, uncertainty bounds and the calculation version, or copy a structured text summary. On supported devices, Apple Intelligence can draft a plain-language analysis that never alters the calculated numbers. REFERENCE LIBRARY Read bundled historical and technical PDFs with page bookmarks, find and go-to. Browse fifty curated web links covering tools, research, forums and video from every perspective, plus references, worked formulas for the calculator, map and explorer, and an indexed glossary of more than eighty terms. YOUR DATA Saved observations, rulers, points, links, imported PDFs and reading positions sync privately through iCloud on signed-in devices, with portable backup and restore. No account, tracking or advertising. Curvature does not tell you what to believe. It shows what each model predicts, how that was calculated and where the model stops.