Final answer:
Sides form arithmetic progressions while vertices form geometric progressions.
Step-by-step explanation:
Mathematics is the subject being referred to in this question.
When it comes to sides and vertices, sides form series of arithmetic progressions while vertices form series of geometric progressions. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
For example, consider the sides and vertices of a square:
- The sides of a square form an arithmetic progression - each side is offset by a constant value (the length of one side).
- The vertices of a square form a geometric progression - each vertex is obtained by multiplying the previous vertex by a fixed ratio (90 degrees).