Have you ever wondered what happens to the shape and size of a figure when it's scaled up or down? How does the perimeter and area change? Let's delve into the fascinating concept of geometric dilations and discover how a simple scale factor can transform a shape entirely.
Have you ever pondered over the enigmatic similarity between a tree and its branches? It's as if the tree is a microcosm of itself, a concept that bewilders and fascinates us. But why does this pattern repeat itself in nature? What is the peculiar charm of these self-similar shapes that captivate both mathematicians and laymen alike? Let's dive into the rabbit hole of fractals and uncover the mystery behind their omnipresence.