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abhilash

The **haversine formula** calculates the shortest distance between two points, whose latitudes and longitudes are known, in a sphere. When used for points on the Earth, the calculated distance is approximate as the formula assumes the Earth to be a perfect sphere.

The haversine formula can be expressed as follows:

The central angle haversine can be computed as follows:

The values in the formula above stand for the following:

- $lat_2$ and $lat_1$ are the latitudes of the two points.
- $long_2$ and $long_1$ are the longitudes of the two points.
- $d$ is the distance between the two coordinates.
- $r$ is the radius of the earth, that is, 6,371 kilometers.

We can derive the haversine formula to calculate the distance d between two points as follows:

```
a = sin²(Δlat/2) + cos(lat1).cos(lt2).sin²(Δlong/2)
c = 2.atan2(√a, √(1−a))
d = R.c
```

In the formula above, the values are calculated as follows:

`Δlat = lat1 − lat2`

`Δlong = long1 − long2`

`R`

is the radius of the earth, that is, 6,371 kilometers.

import math def haversine_distance(coord1: tuple, coord2: tuple): lon1, lat1 = coord1 lon2, lat2 = coord2 R = 6371000 phi_1 = math.radians(lat1) phi_2 = math.radians(lat2) delta_phi = math.radians(lat2 - lat1) delta_lambda = math.radians(lon2 - lon1) a = math.sin(delta_phi / 2.0) ** 2 + math.cos(phi_1) * math.cos(phi_2) * math.sin(delta_lambda / 2.0) ** 2 c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a)) meters = R * c km = meters / 1000.0 meters = round(meters, 3) km = round(km, 3) miles = km * 0.621371 print(f"Distance: {meters} m") print(f"Distance: {km} km") print(f"Distance: {miles} miles") if __name__ == "__main__": lat1 = 43.2341 lon1 = 0.5463 lat2 = 58.1234 lon2 = 88.9421 coord1 = (lat1, lon1) coord2 = (lat2, lon2) print("Distance between", coord1, "and" , coord2, ":") haversine_distance(coord1, coord2)

- Line 8: We define the radius of the earth.
- Lines 9-10: The latitude values are converted to radians.
- Line 12: The difference between the latitudes is calculated.
- Line 13: The difference between the longitudes is calculated.
- Lines 15, 17, 19: The formula in the overview section is implemented to get the distance in meters.
- Line 20: The distance is calculated in kilometers.
- Line 22, 23: The distances are rounded to 3 decimal points.
- Line 24: The distance is calculated in miles.
- Lines 25-27: The distance in different units is printed.
- Lines 31-37: The coordinates are defined.
- Line 39:
`haversine_distance()`

method is invoked to find the haversine distance.

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