Paano Kalkulahin si Haversine
Ano ang Haversine?
The Haversine formula calculates the great-circle distance between two points on a sphere (like Earth) from their latitude and longitude. It is used in navigation, mapping, and GPS applications.
Pormula
a = sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2); d = 2R·arcsin(√a)
- φ₁, φ₂
- latitude of points 1 and 2 (radians)
- Δφ
- difference in latitude (radians)
- λ₁, λ₂
- longitude of points 1 and 2 (radians)
- Δλ
- difference in longitude (radians)
- R
- Earth radius (km (≈6371)) — or miles (≈3959)
- d
- great-circle distance (km or miles)
Step-by-Step na Gabay
- 1a = sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlon/2)
- 2c = 2×atan2(√a, √(1−a))
- 3d = R × c, where R = 6371 km (Earth radius)
- 4Gives shortest path along Earth's surface
Mga Nalutas na Halimbawa
Input
London (51.5°N,0.1°W) to New York (40.7°N,74°W)
Resulta
≈ 5,570 km / 3,461 miles
Input
Paris to Berlin
Resulta
≈ 878 km
Mga madalas itanong
What is a great circle?
The shortest path between two points on a sphere. On Earth, that's the shortest route between two locations.
Why not use Euclidean distance for GPS?
Earth is curved (sphere). Euclidean distance (straight line) ignores the curvature and gives incorrect results.
Is haversine the only way to calculate geographic distance?
No, but it's accurate, numerically stable, and avoids singularity issues of other formulas.
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