Map makers want to make maps that do three things (amongst others):

Unfortunately no map can simultaneous have all three so maps can only approximate the real geometry of a curved surface.

Map making, therefore, is a compromise so there are many different named projections.

Here are a few.

rhumb lines are represented
by straight segments

shape of circles
are conserved

Hammer projection is an
equal-area map projection

Conical Gnomonic projection
displays all great circles as straight lines.

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