diff --git a/Different Ways of Calculating Pi.ipynb b/Different Ways of Calculating Pi.ipynb new file mode 100644 index 0000000..ad00f1d --- /dev/null +++ b/Different Ways of Calculating Pi.ipynb @@ -0,0 +1,173 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.141592653589793" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import math\n", + "math.pi" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implementing the methods for calculating pi from the WikiHow article on the subject \n", + "https://www.wikihow.com/Calculate-Pi#:~:text=The%20circumference%20of%20a%20circle%20is%20found%20with%20the%20formula,result%20should%20be%20roughly%203.14.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Gregory-Leibniz Series**\n", + "\n", + "This series takes many calculations to reach even a few accurate decimal places of pi. The calculation is done by alternating adding and subtracing calculations of 4 divided by an odd integer, starting with 0 add 4 divided by 1. According to the WikiHow article, it takes 500,000 calculations to obtain 5 accurate digits of pi. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.14159264958921" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def GregoryLeibnizSeries(endInteger):\n", + " pi = 0\n", + " current_operator = \"+\"\n", + " for i in range(1, endInteger, 2):\n", + " current_calculation = 4/i\n", + " if current_operator == \"+\":\n", + " pi += current_calculation\n", + " current_operator = \"-\"\n", + " elif current_operator == \"-\":\n", + " pi -= current_calculation\n", + " current_operator = \"+\"\n", + " return(pi)\n", + "\n", + "GregoryLeibnizSeries(500000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Nilakantha Series**\n", + "\n", + "This series converges faster than the *Gregory-Leibniz Series*, but is a mildly more complex calculation. Again, alternating addition and subtraction, starting with addition, and dividing 4 by a value. This time, the value 4 is divided by is three numbers multiplied together, starting with an even number and the next two numbers are that even number plus 1 and plus 2. So, the first two calculations are starting with 3, add 4 divided by (2 × 3 × 4), and then subtract 4 divided by (4 × 5 × 6). " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.141592653589787" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def NilakanthaSeries(endInteger):\n", + " pi = 3\n", + " current_operator = \"+\"\n", + " for i in range(2, endInteger, 2):\n", + " current_calculation = 4/(i*(i+1)*(i+2))\n", + " if current_operator == \"+\":\n", + " pi += current_calculation\n", + " current_operator = \"-\"\n", + " elif current_operator == \"-\":\n", + " pi -= current_calculation\n", + " current_operator = \"+\"\n", + " return(pi)\n", + "\n", + "NilakanthaSeries(500000000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Pi using sine** \n", + "\n", + "This one is easier, pick a big number, multiple that big number by the sine of 180 / big number, sine needs to be in degrees. In the python code below you can see the sin calculation is converting degrees to radians with `math.radians` because trig functions in the `math` library calculate with radians. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.141592653589793" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import math\n", + "\n", + "def LimitsCalculation(BigNumber):\n", + " current_calculation = BigNumber * math.sin(math.radians(180/BigNumber))\n", + " return(current_calculation)\n", + "\n", + "LimitsCalculation(900000000000)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}