{
"cells": [
{
"cell_type": "markdown",
"id": "e75455a5-ad8e-4a0b-bd1e-15503b47a997",
"metadata": {},
"source": [
"# Graphing using Matplotlib and Creating Interactive Plots and Animations\n",
"\n",
"This data set comes from plotting the Prime numbers as the raduis and angle in polar coordinates. \n",
"The spiral artifacts at smaller prime numbers and the transition seen to rays is documented here:\n",
"[Meaning of rays in polar plot of prime numbers](https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers)\n",
"Asked by user dwymark and answer by Greg Martin. A complete video animation and explaination on YouTube channel 3Blue1Brown created by Youtuber Grant Sanderson. The video [Why do prime numbers \n",
"make these spirals? | Dirichlet’s theorem and pi approximations](https://www.youtube.com/watch?v=EK32jo7i5LQ)\n",
"\n",
"## Using Jupyter Lab to create a dataset and pandas dataframe\n",
"### Introduction to 2d Plotting"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "20e245ca-9ce5-49e6-ba4e-043b99118093",
"metadata": {},
"outputs": [],
"source": [
"import sympy\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.widgets import Slider\n",
"from ipywidgets import interact, widgets\n",
"\n",
"%matplotlib widget\n",
"plt.style.use('dark_background')"
]
},
{
"cell_type": "markdown",
"id": "aa135126-db70-46ad-91bd-7869bcb71d1b",
"metadata": {},
"source": [
"Prime numbers between 0 and 100 using the [sybmolic math library](https://www.sympy.org/en/index.html)."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5eeec12e-fac3-4ba9-8350-c4f0d838dcdf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\n",
"Number of primes under 100 is 25\n"
]
}
],
"source": [
"num = 100\n",
"primes=list(sympy.primerange(0, num))\n",
"print(primes)\n",
"print(\"Number of primes under\", num, \"is\", len(primes))"
]
},
{
"cell_type": "markdown",
"id": "f98f2958-0fdb-4ba0-822e-dce1aaafe81b",
"metadata": {},
"source": [
"Convert the primes to a Cartesian coordinate system assuming the prime number represents both the degrees and radius of a polar coordinate.\n",
"\n",
"- x = r cos(θ)\n",
"- y = r sin(θ)\n",
"\n",
"Define a function for X and Y conversion."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cca9f6e4-d593-46e8-9f32-c0e535a88c12",
"metadata": {},
"outputs": [],
"source": [
"def Xcartesian_from_polar_coordinates(x):\n",
" return x * np.cos(x)\n",
"def Ycartesian_from_polar_coordinates(y):\n",
" return y * np.sin(y)"
]
},
{
"cell_type": "markdown",
"id": "8d6abd63-f092-4ce8-8541-9ce77f071ef5",
"metadata": {},
"source": [
"Create a [pandas](https://pandas.pydata.org/docs/) dataframe of prime numbers, labeling the column \"Primes\" and display the first 5 rows."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "dcf690ac-4ad7-4ba7-bf98-9a247d0b5123",
"metadata": {},
"outputs": [
{
"data": {
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