1) Input coordinates
Start: Les Sables-d’Olonne φ₁ = 46.494953°, λ₁ = -1.792091°
End: Saint-François φ₂ = 16.252360°, λ₂ = -61.273320°
2) Pythagoras flat approximation (local planar)
$$\Delta\phi = \phi_2 - \phi_1 = 16.25236 - 46.494953 = -30.242593^\circ$$
$$\Delta\lambda = \lambda_2 - \lambda_1 = -61.27332 - (-1.792091) = -59.481229^\circ$$
$$\text{distance} = \sqrt{ (\Delta\phi \cdot R)^2 + (\Delta\lambda \cdot R \cos\bar{\phi})^2 }$$
$$\bar{\phi} = \frac{\phi_1 + \phi_2}{2} = 31.373657^\circ$$
$$R = 6371\ \text{km},\quad \Delta\phi_{\text{rad}} = -0.5282,\quad \Delta\lambda_{\text{rad}} = -1.0381,\quad \bar{\phi}_{\text{rad}} = 0.5475$$
$$d \approx \sqrt{ (\Delta\phi_{\text{rad}} \cdot R)^2 + (\Delta\lambda_{\text{rad}} \cdot R \cdot \cos \bar{\phi}_{\text{rad}})^2 } \approx 6260\ \text{km}$$
Pythagoras assumes a flat surface; good for short distances.
3) Haversine formula (spherical Earth)
$$\Delta\phi = \phi_2 - \phi_1 = 0.283657 - 0.811490 = -0.527833\ \text{rad}$$
$$\Delta\lambda = \lambda_2 - \lambda_1 = -1.069427 - (-0.031284) = -1.038143\ \text{rad}$$
$$a = \sin^2(\Delta\phi/2) + \cos\phi_1 \cos\phi_2 \sin^2(\Delta\lambda/2)$$
$$a = \sin^2(-0.2639165) + \cos(0.81149) \cos(0.283657) \sin^2(-0.5190715) \approx 0.2043$$
$$c = 2 \arctan2(\sqrt{a}, \sqrt{1-a}) = 0.9450\ \text{rad}$$
$$d = R \cdot c = 6371 \cdot 0.9450 \approx 6020\ \text{km}$$
Haversine assumes a spherical Earth; more accurate for long distances.