On Valentine's day, we were given a geometry problem. It consisted of three shapes, a circle, a circular heart, and a wonky deformed heart (One hump was smaller than the other). The questions was, by making the circle into a heart, has the circle gotten smaller? Does the circumference and area change? We noticed by comparing the heart to the circle that circumference didn't change, but the area did. When we found the area of the wonky heart, it was the same thing: different area, same circumference. Why did this pattern show up? And then it hit me: All we've done is change the position of the line. We haven't stretched it or squished it, just moved it a little. Had I not noticed the pattern, I wouldn't have come to that conclusion.