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   "source": [
    "## Lab 11 ###"
   ]
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    "## Consider the following information\n",
    "\n",
    "#### 1. References for group calculations:\n",
    "\n",
    "https://pandas.pydata.org/pandas-docs/version/1.2/reference/api/pandas.core.groupby.GroupBy.mean.html\n",
    "\n",
    "https://pandas.pydata.org/pandas-docs/version/1.2/reference/api/pandas.core.groupby.GroupBy.min.html\n",
    "\n",
    "#### 2. main libraries to be imported:\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "file=\"https://github.com/masterfloss/sustainability/raw/refs/heads/main/lisboa.xlsx\"\n",
    "data = pd.read_excel(file)\n",
    "\n",
    "#### 3. distance between two points on the Earth's surface given their latitude and longitude in decimal degrees.\n",
    "\n",
    "The function you provided is known as the **Haversine formula**, which calculates the great-circle distance between two points on the Earth's surface given their latitude and longitude in decimal degrees. Here's a breakdown of the mathematical formulas extracted from the function:\n",
    "\n",
    "1. **Input Parameters:**\n",
    "\n",
    "   - lat1: Latitude of the first point (in degrees).\n",
    "   - lon1: Longitude of the first point (in degrees).\n",
    "   - lat2: Latitude of the second point (in degrees).\n",
    "   - lon2: Longitude of the second point (in degrees).\n",
    "\n",
    "\n",
    "2. **Earth's Radius:**\n",
    "   - R = 6371 km (average radius of the Earth).\n",
    "\n",
    "3. **Differences in Latitude and Longitude:**\n",
    "\n",
    "\\begin{align}\n",
    "   \\Delta \\text{lat} = \\text{lat2} - \\text{lat1}\\\\\n",
    "   \\Delta \\text{lon} = \\text{lon2} - \\text{lon1}\n",
    "\\end{align}\n",
    "\n",
    "4. **Convert Degrees to Radians:**\n",
    "\\begin{align}\n",
    "   \\ dlat = \\text{radians}(\\Delta \\text{lat}) \\\\\n",
    "   \\ dlon = \\text{radians}(\\Delta \\text{lon})\n",
    "\\end{align}\n",
    "5. **Haversine Formula:**\n",
    "\\begin{align}\n",
    "   a = \\sin^2\\left(\\frac{dlat}{2}\\right) + \\cos(\\text{radians}(\\text{lat1})) \\cdot \\cos(\\text{radians}(\\text{lat2})) \\cdot \\sin^2\\left(\\frac{dlon}{2}\\right)\n",
    "\\end{align}\n",
    "   \n",
    "6. **Central Angle (c):**\n",
    "\\begin{align}\n",
    "   c = 2 \\cdot \\text{atan2}\\left(\\sqrt{a}, \\sqrt{1 - a}\\right)\n",
    "\\end{align}\n",
    "\n",
    "7. **Distance (d):**\n",
    "\\begin{align}\n",
    "   d = R \\cdot c\n",
    "\\end{align}\n",
    "   where \\( d \\) is the great-circle distance between the two points.\n",
    "\n",
    "The overall Haversine formula to compute the distance between two points on the Earth's surface is:\n",
    "\\begin{align}\n",
    "d = 2R \\cdot \\text{atan2}\\left(\\sqrt{a}, \\sqrt{1 - a}\\right)\n",
    "\\end{align}\n",
    "where \\( a \\) is calculated as described above.\n",
    "\n",
    "\n"
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    "## Answer to the following questions separatly:\n",
    "\n",
    "\n",
    "#### 1. Import necessary libraries and read import dataset\n",
    "\n",
    "#### 2. Separate points of interest (POIs) and Metro station data\n",
    "\n",
    "#### 3. Define a Haversine function (lat1, lon1, lat2, lon2) to calculate the distance between two coordinates\n",
    "\n",
    "#### 4. Combine the Metro and POI datasets into a new dataset\n",
    "\n",
    "#### 5. Create a new column for distances by applying the Haversine function. Use the pandas apply method: \n",
    "https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.apply.html\n",
    "\n",
    "#### 6. Calculate the distance to the closest metro station for each POI\n",
    "\n",
    "#### 7. Calculate the average distance of each POI to all metro stations\n"
   ]
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