{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "まずは２次元球(円)のシミュレーションから"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1419336"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "N = 10000000\n",
    "for i in 1:N\n",
    "    x = rand()\n",
    "    y = rand()\n",
    "    if x^2 + y^2 < 1\n",
    "        count = count + 1\n",
    "    end\n",
    "end\n",
    "print((4*count)/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi * 1^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3次元球のシミュレーション"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.1888864"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "N = 10000000\n",
    "for i in 1:N\n",
    "    x = rand()\n",
    "    y = rand()\n",
    "    z = rand()\n",
    "    if x^2 + y^2 + z^2 < 1\n",
    "        count = count + 1\n",
    "    end\n",
    "end\n",
    "print((8*count)/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.1887902047863905"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(4/3) * pi*1^3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.550164039877345"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n=15\n",
    "((pi^(n/2))/gamma((n/2)+1))*1^n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "n次元球のシミュレーション"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.43712\n",
      "2.550164039877345\n"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "N = 100000　# 繰り返し回数（シミュレーション回数）\n",
    "n = 10 # 次元数\n",
    "for i in 1:N\n",
    "    if sum(rand(1,n).^2) < 1\n",
    "        count = count + 1\n",
    "    end\n",
    "end\n",
    "println((2^n*count)/N) # シミュレーションの値\n",
    "println(((pi^(n/2))/gamma((n/2)+1))*1^n)　#実際の値"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Julia 0.6.3",
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  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
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