{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Convergence to $\\pi$\n",
"\n",
"Finding numerical approximations to $\\pi$ has fascinated people for millenia. One famous formula is\n",
"\n",
"$ \\displaystyle \\frac{\\pi^2}{6} = 1 + \\frac{1}{2^2} + \\frac{1}{3^2} + \\cdots. $\n",
"\n",
"\n",
"Say $s_k$ is the sum of the first $k$ terms of the series above, and $p_k = \\sqrt{6s_k}$. Here is a fancy way to compute these sequences in a compact code."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=1}"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = [1/k^2 for k=1:100] \n",
"s = cumsum(a) # cumulative summation\n",
"p = @. sqrt(6*s)\n",
"\n",
"using Plots\n",
"plot(1:100,p,m=:o,leg=:none,xlabel=\"k\",ylabel=\"p_k\",title=\"Sequence convergence\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This graph suggests that $p_k\\to \\pi$ but doesn't give much information about the rate of convergence. Let $\\epsilon_k=|\\pi-p_k|$ be the sequence of errors. By plotting the error sequence on a log-log scale, we can see a nearly linear relationship."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=1}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ep = @. abs(pi-p) # error sequence\n",
"plot(1:100,ep,m=:o,l=nothing,\n",
" leg=:none,xaxis=(:log10,\"k\"),yaxis=(:log10,\"error\"),title=\"Convergence of errors\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This suggests a power-law relationship where $\\epsilon_k\\approx a k^b$, or $\\log \\epsilon_k \\approx b (\\log k) + \\log a$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Array{Float64,1}:\n",
" -0.1823752497283019\n",
" -0.9674103233127926"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k = 1:100\n",
"V = [ k.^0 log.(k) ] # fitting matrix\n",
"c = V \\ log.(ep) # coefficients of linear fit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In terms of the parameters $a$ and $b$ used above, we have"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a, b) = (exp(c[1]), c[2]) = (0.8332885904225771, -0.9674103233127926)\n"
]
}
],
"source": [
"@show (a,b) = exp(c[1]),c[2];"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's tempting to conjecture that $b\\to -1$ asymptotically. Here is how the numerical fit compares to the original convergence curve."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=2}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot!(k,a*k.^b,l=:dash)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (faststart)",
"language": "julia",
"name": "julia-fast"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}