User talk:Ylee15

Hi, this is my Talk page. Thanks. Ylee15 (talk) 15:52, 11 August 2022 (UTC)

Vincenty formula for great-circle distance
In Great-circle distance, the following formula is introduced as a formula that works for *all distances*.


 * $$\Delta\sigma =

\arctan \frac{\sqrt{\left(     \cos\phi_2\sin(\Delta\lambda)\right)^2 + \left(\cos\phi_1\sin\phi_2 - \sin\phi_1\cos\phi_2\cos(\Delta\lambda)   \right)^2}} {\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos(\Delta\lambda)}. $$

But, it seems not. For example, if we have $$\Delta\lambda = 0$$, we have

\Delta\sigma = \arctan \frac{|\sin(\theta_1-\theta_2)|}{\cos(\theta_1-\theta_2)} $$ Let's say $$\theta_1 = \pi/2$$ and $$\theta_2=-\pi/2$$, then we should have $$\Delta\sigma=\pi$$. But, the formula above yields $$0$$. Ylee15 (talk) 16:11, 11 August 2022 (UTC)