Globes with geographical maps are conventionally made by gluing paper sheets of a specific form on a spherical surface. Such paper sheets (segments on the sphere cut along the meridians) are called gores. For those who are interested, there is a nice video about globes production: https://www.youtube.com/watch?v=ymjWeQhic0s&t=307s&abchannel=InsiderBusiness.

What is the shape of these gores? By what mathematical functions the two edges of the gore are defined? E.g., parabolic, exponential, linear, etc. You will get an extra point if you write down these functions in the explicit form (with being the argument).