In the Dark with an Elephant
Posted October 2, 2000 as a Math Forum EPoW

Introduction: In this problem, students were asked to investigate how the appearance of a graph changed, based on the scale of the graph and the region being viewed.

Where's the Math: This problem gives students experience in manipulating graphs by changing domain and range values for the viewing window, which can easily be carried over to more powerful tools such as graphing calculators. It also allows students to become familiar with the Cartesian coordinate system. The questions encourage thought about how the shape of specific areas of a graph are not necessarily representative of the shape of the entire graph. Standards: Algebra, geometry Role of Components: A SimCalc graph displays the function. ImageView components display the target GIF images. A hidden FunctionEntry is used to set the function displayed in the graph. NumberEntry components allow the user to input the domain and range. The Bundle component (Data Recorder) collects the inputted values for each attempt. Standard Swing components are used for the buttons and the label.

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Sample submitted solutions:

From:  Alex, age 14
School:  McLean High School, McLean, Virginia

1. What are the values for domain and range that you found to make the working window look like:
* View A: x min: 2, x max: 4, y min: 2, y max: 5
* View B: x min: -2, x max: 2, y min: -12, y max: 12
* View C: x min: -9, x max: -1, y min: -8, y max: 1

2. Describe a strategy to make a curve look like a line.
Look at the curve from a different point of view than ordinary, such as from above. If you look at the curve from overhead, it looks like a line, almost 2-D.

3. Using what you did in this PoW, explain why people might have believed the world was flat.
People might have thought that the world was flat because their point of view was different from a different angle. They couldn't see everything completely.

1. What are the values for domain and range that you found to make the working window look like:
* View A: X min: -5. X max: -3.5 Y min: -.7 Y max: -.1
* View B: X min: -2 X max: 2 Y min: -4 Y max: 4
* View C: X min: -5 X max: -2 Y min: -1 Y max: .7

2. Describe a strategy to make a curve look like a line.
If you zoom in really really far, a curve can look like a line.

3. Using what you did in this POW, explain why people might have believed the world was flat.
When you look at something curved very close up, it can look flat. When you look at one little piece of the world, it looks flat, but if you could see the whole world at one time, it would look round.

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