Math Problem Statement

2.) Create contour plot using the following Elevation data sets.

Grid coordinates:

x = linspace(0, 100, 10); // X coordinates, from 0 to 100 meters

y = linspace(0, 100, 10); // Y coordinates, from 0 to 100 meters

Elevation Data set

Z = [50, 55, 60, 65, 68, 70, 72, 74, 76, 80; 48, 52, 57, 63, 67, 69, 71, 73, 75, 78; 46, 50,

55, 60, 64, 68, 70, 72, 74, 76; 45, 49, 53, 58, 63, 66, 68, 70, 72, 75; 43, 47, 51, 56, 61,

64, 67, 69, 71, 73; 42, 46, 50, 54, 59, 62, 65, 68, 70, 72; 40, 44, 48, 52, 57, 61, 64, 66,

69, 71; 39, 43, 47, 51, 55, 59, 62, 64, 67, 69; 37, 41, 45, 50, 54, 58, 60, 63, 66, 68; 35,

40, 44, 49, 53, 56, 59, 62, 65, 67];

Solution

To create a contour plot using the provided elevation dataset, you can use the following Python code with libraries such as NumPy and Matplotlib. Here’s how to do it:

python
import numpy as np import matplotlib.pyplot as plt # Grid coordinates x = np.linspace(0, 100, 10) # X coordinates y = np.linspace(0, 100, 10) # Y coordinates # Elevation data set Z = np.array([ [50, 55, 60, 65, 68, 70, 72, 74, 76, 80], [48, 52, 57, 63, 67, 69, 71, 73, 75, 78], [46, 50, 55, 60, 64, 68, 70, 72, 74, 76], [45, 49, 53, 58, 63, 66, 68, 70, 72, 75], [43, 47, 51, 56, 61, 64, 67, 69, 71, 73], [42, 46, 50, 54, 59, 62, 65, 68, 70, 72], [40, 44, 48, 52, 57, 61, 64, 66, 69, 71], [39, 43, 47, 51, 55, 59, 62, 64, 67, 69], [37, 41, 45, 50, 54, 58, 60, 63, 66, 68], [35, 40, 44, 49, 53, 56, 59, 62, 65, 67] ]) # Create contour plot plt.figure(figsize=(8, 6)) plt.contourf(x, y, Z, cmap='viridis') # Filled contours plt.colorbar(label='Elevation (meters)') plt.title('Contour Plot of Elevation Data') plt.xlabel('X Coordinate (meters)') plt.ylabel('Y Coordinate (meters)') plt.grid() plt.show()

Explanation:

  1. Data Preparation: The grid coordinates and elevation data are set up.
  2. Contour Plotting: contourf is used for filled contour plots, and a color bar is added for reference.
  3. Visualization: The plot includes labels for axes and a title.

Would you like further details on any specific part of this process, or do you have questions? Here are some related topics you might consider:

  1. How to customize the color map for better visualization?
  2. Ways to save the plot as an image file.
  3. Additional plotting techniques for elevation data.
  4. How to interpolate missing elevation data points.
  5. The significance of contour lines in topography.

Tip: Explore different colormaps in Matplotlib for better representation of elevation changes!

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Math Problem Analysis

Mathematical Concepts

Contour Plotting
Data Visualization
Grid Coordinates

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12