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What if you make the rope into a circle?
A circle encloses the most area for a given perimeter, more than a square. A square's corners are wasted, but a circle has none. Elementary math 3.
The Duowenwen team · Updated
This is the third question in the elementary math chain of the question map. The first two showed that the same perimeter can give different areas, and that among rectangles the square is the biggest. This one looks at the circle.
What if you make the rope into a circle?
For a given perimeter, a circle encloses the most area, even more than a square. Here's one way to think about it: a square's corners are "wasted." The rope goes out to the corner and back without enclosing much extra space there. A circle has no corners, and every bit of the rope is pushing outwards. That's why water drops and soap bubbles are round: they're using the least "skin" to wrap up the most inside.
What if…?
This chain is yours to carry on from here. Turn it around: if the area stays the same, which shape has the shortest perimeter? Why?
Next: type your guess into Duowenwen and let it start from "Why?"