why does when we walk 10km to the south, then another 10km to the east, and another 10km to the south, we finally reach the initial point of our journey in the North Pole?

I don't think there is an answer for that????

bcoz of the latitudes and longitudes.

The reason why you would end up back at the initial point of your journey in the North Pole after walking 10km to the south, then 10km to the east, and then 10km to the south again is due to the unique geometry of the Earth's surface.

To understand this, let's break down the journey step-by-step:

1. Walking 10km to the south: When you walk 10km directly south, you are moving away from the North Pole towards a point closer to the South Pole.

2. Walking 10km to the east: After moving 10km to the south, you then walk 10km directly east. This means you are moving parallel to the equator, which is perpendicular to the lines of longitude. So, your eastward movement does not change your latitude, but it does change your longitude, putting you 90 degrees east of your initial position.

3. Walking 10km to the south again: Finally, you walk another 10km directly south. At this point, you are still moving away from the North Pole and getting closer to the South Pole.

Now, let's think about the effects of these movements:

- When you walked 10km to the south, you moved 10km away from the North Pole.
- When you walked 10km to the east, you changed your longitude but did not change your latitude.
- When you walked 10km to the south again, you moved 10km closer to the South Pole.

Here's the crucial part: When you reach the South Pole, you have circumnavigated the Earth's globe once. Continuously moving south from the North Pole essentially takes you around the Earth in a circular path. So, after making a full circle around the South Pole (which covers a distance of the Earth's circumference), walking 10km to the east from any point would, in fact, bring you back to your starting point.

In summary, the combination of southward movements and eastward movement eventually takes you around the Earth in a circle, leading you back to your starting point in the North Pole. This happens due to the Earth's spherical shape and the way latitude and longitude lines work.