It's called the divider. The main purpose of it is to measure distance between two points where you can't use a ruler. Like a curved surface or any interior part of a machinery etc. It's called a divider because we can use it to divide a line into equal parts. Let's say there's a line of 10cm length and you want to fix stop points at 1cm intervals. You simply set the divider at 1cm wide and easily mark the points. It is also used to compare/transfer measurements. Like if you have a 2cm wide wooden log and you are trying to shine another wooden plank to 2cm wide. You just measure the width of first plank and after shining 2nd one you compare it with the divider to check if you have reached same width.
It's not just a mathematical tool. It's a design and crafts tool as well. Used in various industries, designing and craftsmanship.