{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyMUqMHL1ub+cwn+7CgQSepv",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
" "
]
},
{
"cell_type": "markdown",
"source": [
"# Problem Statement: Drawing a Polygon Using Python\n",
"\n",
"Objective: Create a Python script that draws a regular polygon (e.g., triangle, square, pentagon) based on user input, using the matplotlib library.\n",
"\n",
"## Requirements:\n",
"\n",
"1. User Input:\n",
"\n",
" * Prompt the user to enter the number of sides of the polygon (an integer greater than 2).\n",
"Prompt the user to enter the side length of the polygon.\n",
"\n",
"\n",
"2. Drawing the Polygon:\n",
"\n",
" * Use the matplotlib library to draw the polygon.\n",
"Ensure that the polygon is a regular polygon (all sides and angles are equal).\n",
"\n",
"3. Visualization:\n",
"\n",
" * Display the polygon with equal scaling on both the x and y axes.\n",
"\n",
" * Mark the vertices of the polygon with dots.\n",
"\n",
"4. Output:\n",
"\n",
" * The script should display the drawn polygon in a window.\n",
"\n",
"Example:\n",
"\n",
"* If the user inputs 5 for the number of sides and 1 for the side length, the script should display a regular pentagon with each side of length 1.\n",
"\n",
"Guidelines:\n",
"\n",
"* Ensure your code is well-commented and organized.\n",
"Handle invalid input gracefully (e.g., non-integer inputs, number of sides less than 3).\n"
],
"metadata": {
"id": "VkDPjcnyV72S"
}
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 452
},
"id": "TwWwuC5RU_RR",
"outputId": "66979ab0-e95d-4f01-e43a-005d5b409f10"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"# Function to draw a polygon\n",
"def draw_polygon(num_sides, side_length):\n",
" angle = 2 * np.pi / num_sides\n",
" points = [\n",
" (np.cos(i * angle) * side_length, np.sin(i * angle) * side_length)\n",
" for i in range(num_sides)\n",
" ]\n",
" points.append(points[0]) # Close the polygon by adding the first point at the end\n",
" return zip(*points)\n",
"\n",
"# Set the number of sides and the side length\n",
"num_sides = 6\n",
"side_length = 1 # Length will be scaled automatically\n",
"\n",
"# Get the polygon points\n",
"x, y = draw_polygon(num_sides, side_length)\n",
"\n",
"# Plot the polygon\n",
"plt.figure()\n",
"plt.plot(x, y, marker='o')\n",
"plt.title(f'{num_sides}-sided Polygon')\n",
"plt.axis('equal') # Equal scaling for x and y axes\n",
"plt.show()\n"
]
}
]
}