2.5 - What Do You Think?

Q2.15: What does it mean to you that an object has a fractional dimension? (HINT: The following questions could prompt their thinking: How does the object fill space? Is its use of space dense or sparse? Are its edges smooth or jagged? What is similar throughout different parts of the object? What is random or different throughout different parts of the object? How does the whole object compare with individual parts of the object? What geometric shapes do you see in the object: circles, lines, ovals, spheres?)

Q2.16: Is there a quantitative difference between measuring the coastline by the "ruler method'', "box method'', and "circle method''? If so, can you explain why? Why would scientists need all three methods (i.e., why don't they just pick the "best one'')? HINT: Think of some examples from nature which would be better suited towards a particular method.

Q2.17: In the beginning of this unit, we talked about the length of the coastline as measured by various observers (e.g., an automobile, bicyclist, jogger and bird). Can you say whether the fractal dimension of the coastline measured by these observers would be the same or different? How does it change (or not change)? Which observer would get the most accurate fractal dimension?

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