Can the State of Ohio Be Represented on a Standard Piece of Paper?
The state of Ohio, known for its unique geographical layout and historical significance, presents an interesting challenge when it comes to map representation. This article delves into the question: can the entire state of Ohio be represented on an 8.5 inches by 11 inches sheet of paper?
Understanding the Geometry of Ohio
The greatest distance between any two points within the state of Ohio is 245 miles. This means that for a comprehensive map, the state must be represented within a circle with a diameter of 245 miles. However, when it comes to representation on a 8.5 by 11 inches piece of paper, the key lies in determining the appropriate scale.
Map Representation on 8.5 by 11 Inches Paper
The 8.5 by 11 inches piece of paper refers to its horizontal and vertical dimensions. To fit the state within these dimensions, we need to calculate the scale. Since the longest dimension of the paper is 11 inches, we consider this to be the primary axis for representation. However, we must also ensure that the shorter dimension (8.5 inches) can adequately represent the state.
Option 1 - Uniform Scale
The scaling can be calculated as follows:
11 inches (horizontal scale) 245 miles
1 inch 245 / 11 miles ≈ 22.27 miles
Around 22.5 miles has been suggested. Similarly, for the 8.5 inches vertical dimension:
8.5 inches (vertical scale) 245 miles
1 inch 245 / 8.5 miles ≈ 28.82 miles
Rounded to the nearest whole number, 29 miles is used.
When using a uniform scale, the state might need to be stretched or compressed to fit perfectly within the horizontal and vertical dimensions of the paper. This suggests that a uniform scale might not be ideal for representing the state accurately.
A Second Option - Different Scales for Horizontal and Vertical
An alternative approach involves using different scales for the horizontal and vertical dimensions. Here, we use the full 11 inches horizontally:
11 inches (horizontal scale) 245 miles
1 inch 245 / 11 miles ≈ 22.27 miles (rounded to 22.5 or 23 miles)
For the vertical dimension, we continue with the previously calculated 29 miles as the scale.
This method would provide a more accurate representation of the state but could result in distortion due to the uneven scaling.
Lack of Exercise 1 Information
Unfortunately, the article begins with a reference to 'Exercise 1' without providing any specific details. This omission makes it difficult to determine the scale used in the exercise and to answer the question comprehensively. The absence of this crucial information means we cannot definitively state whether the state can be fully represented on the paper or not.
Alternatively, if the scale from Exercise 1 were provided, we could accurately determine the distance that would be represented on the paper and whether the entire state can fit within the given dimensions.
Conclusion
Whether the state of Ohio can be entirely represented on an 8.5 by 11 inches piece of paper hinges on the chosen scale. Uniform scaling or using different scales for the horizontal and vertical dimensions are two approaches. However, without specific details from Exercise 1, it is challenging to provide a definitive answer. The use of a uniform scale might require the state to be stretched or compressed, while different scales offer a more accurate but potentially distorted representation.