{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "252388e4-22ce-4dc6-b679-3b54b1224371",
   "metadata": {},
   "source": [
    "# Die Kreiszahl π"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c92f62e5-2289-4b1e-9fd1-57a085681cfc",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d65e5d7-ee53-46b4-84d6-53c6c8f26906",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<b>Ziel des Notebooks:</b>\n",
    "\n",
    "- wichtige Herleitungen und Berechnungsschemata von π verstehen\n",
    "- Geschichte und Entwicklung der Naturkonstante \n",
    "\n",
    "<br>\n",
    "    \n",
    "<b>Mathematische Tools:<b>\n",
    "- Geometrie\n",
    "- Stochastik\n",
    "- Reihen und Reihenkonvergenz\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "743f7af8-80e7-48a6-ac9b-186658a5f21f",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5117ac36-c53f-4572-aadd-11c67135d36d",
   "metadata": {},
   "outputs": [],
   "source": [
    "using SymPy, Plots;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04c33abe-b967-45e7-a964-aa662618fa87",
   "metadata": {},
   "source": [
    "In der Antike gab es ein weit verbreitetes Spiel. Die Aufgabe war es, zu einem gegebenen Kreis ein entsprechendes Quadrat zu konstruieren, das exakt den gleichen Flächeninhalt hat wie der Kreis. Als einzige Hilfsmittel zugelassen waren ein Lineal und ein Zirkel. Jahrhunderte lang zerbrach man sich den Kopf über dieses Rätsel. Auch der Mathematiker Archimedes beschäftigte sich mit diesem Problem.\n",
    "\n",
    "Damals vermutete man schon, dass es eine Zahl wie π geben müsse, die das Verhältnis vom Umfang $U$ eines Kreises zu seinem Durchmesser $d$ beschreibt. Obwohl diese Naturkonstante damals noch kaum erforscht war, schaffte Archimedes es als erster Mensch zu beweisen, in welchem Zusammenhang die Volumen der drei geometrischen Körper Kegel, Kugel und Zylinder stehen. Auf diese damals bahnbrechende Erkenntnis war er so stolz, dass er sich auf seinem Grabstein die Umrisse der drei Körper einmeißeln lies. \n",
    "\n",
    "Und das war noch längst nicht seine einzige wichtige geschichtliche und mathematische Erkenntnis. Archimedes schuf einen geometrischen Ansatz zur Berechnung von π, die in den folgenden 2000 Jahren noch von verschiedenen Mathematikern weiterverfolgt wurde."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e28661f-1c16-4f1c-8bbe-31bc86f54381",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Recherche-Aufgabe\n",
    "***\n",
    "Erklären Sie anschaulich (z.B. mit Skizzen), wie Archimedes die Kreiszahl π annäherte und arbeiten Sie die mathematischen Hintergründe genau heraus. Wieso funktionierte seine Idee? Welchen Zahlenwert hatte Archimedes mit dieser Methode berechnet und wie gut war diese Annäherung von Pi?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23de7c5b-3983-41a4-989d-8daebc854e98",
   "metadata": {},
   "source": [
    "Die Bezeichnung \"Pi\" (π) wurde erst im 17. Jahrhundert festgelegt. Bis heute spricht man auch noch von der \"Archimedes-Konstante\"."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cff5a72-1c11-4d26-be53-19b6b6531fac",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56802d87-f12f-4d85-8a00-ef6c3e926cea",
   "metadata": {},
   "source": [
    "Im Jahr 1644 formulierte der Mathematiker Pietro Mengoli das Basler-Problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a12296e3-b04e-447e-a743-917a61c690c3",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Basler-Problem</b> \n",
    "\n",
    "Was ist die Summe der reziproken Quadratzahlen? <br> \n",
    "Oder: Welchen Wert hat die Summe $\\sum\\limits_{n=1}^\\infty \\dfrac{1}{n^2}$?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c02fb23-8a4c-48dd-bf43-23933205c4e8",
   "metadata": {},
   "source": [
    "Im Jahre 1735 wurde erstmals durch Leonard Euler die Lösung gefunden und damit eine besonders elegante Darstellung der Zahl π. Er zeigte nämlich, dass $\\sum\\limits_{n=1}^\\infty \\dfrac{1}{n^2} = \\dfrac{\\pi^2}{6}$."
   ]
  },
  {
   "attachments": {
    "31706f07-1b94-4817-9a4c-c7d69bf277ad.png": {
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X1UHEOUcIIYSQUECDkZAwsPp9pafvdA8IOcBsni6yYYLIwjvV/jT3JCGEEELCAA1Gkj4seUgpnHepHc5QpAQU9LnXi0xuJ7JFKe75ybbfnI2QRFS9SOTghs7+qrfUH9ZhQgghJCyEzmDcu3evu0cyih1LRZYNFVn+gtr+T52gwhmYgxuoP0VEdv7pGN35JbuVSvGfcpzIjG7qYJ9zjpB4lGms/qhyuHGS+s/6SwghhISFUBiMa9eulRUrVsjpp58uJUqUkMaNG8vll18uI0aMkEiEiktmYBXFtZ+6OyQQxSuIlG3h7K8bq4zvZc5+Xvj9SZH5N6odVX8OOVH9V4YAIYkoVcf5v3WeKjYcuCOEEELCQkYbjKNGjZKLL75YqlSpIjVr1pQvv/xSG4jz58+XN954Q8477zxp3bq1vPnmmzQc051StZVNUtLZ3/gD10GlSrmj1B/XqNuUxxmepYNEFj+gdtQzDj1ZpMnzaj+kBuM+rvvMN0pjhhHsU0bjL+4+8WXncpGpqm7t3eyeIIQQQtKXjDUYr7jiCunWrZu88847CY3BGTNmSI8ePaRfv36yYcMG9yxJS7RLm8vK4eoPjfzAlGvj7ij27XJ3csHi+5XB+JjaUbKvcIxIs/+p/ZAai/iePxwhsm2ueyIPrP7QMQB+OFwZS7PdkxnEn+p3nnSUqndvqINc1ruyzdwdxfYl6g/rb1zgFbBlluOGTznlHV3eCCGEFBQZaTDedttt8uqrr6Y0a/jMM89I165dZdmyfHDXIwVDxePUH9c4gQKbH66V2UKlsxyjEVuls9WJXBh5C+8Q+f0ptaPqVdmWIkf+n3pMCedaGNm7RRnXO/YbyLnlt3+JzL1WGQAzRPZsEtm11r2QQezdJrJzhcj8m0X+eFqdyIU8yrYSqXKBs6a2TBN1IqQDDflBsbJOe/fnq+ogH9cHrx+n/mSZAbrgPyI/tRdZ8bI6yLLvTgghB4iMMxjffvttefzxx2OMxWuuuUYmT54s06dPlw8//FD+/ve/S5EiOZWVqVOnSp8+feiemq5U7yNS/BD3QLHmI/Unn3+rNZ84a/MwmzLleJHV76mTISgPmLFo/YXavlT7Fd2TKYDotCbY0MH1lLH4gkjJKs61sFLiUOf/mo9FNv/s7KfKcqWk/vma2nHLUIN73DWfGUYtZfBWv1ztqHZz0X2OEZybetHkGZF2k0RKw2DMB2AA/XaryIxzRP76XJ0IQV01VOgosmezyJKH1UEev9eG71V71klkljLYZ1+iToRITklx+3rUY5KYJY+IfKvadZSRzVPUiWwqJ4SQvJBRBiMMvTvuuCPG4Hvuuef01q5dO2nVqpVet/jee+/J0qVL5auvvpIKFZQibTFmzBh57LHHaDSmIzBU6iOthqsA5MW10gbK1Lx+Ij80EplzhcjKN501RHBFRICObOePZ/cnXC9RSSn9z+1PkRBmyjR1dxR/KWM7VeUJ6x8RHEi/TjWlWOtZ63q1n6Eza0cMFql4vLMPI3j2xSK7VjvHB5oVr4hM7eoYQPA22PijMh7HuBdDwqHq+wG430f2OPu5Yc0IkZnnq/bMbcvKt3f+ZwsVjnX+o4zkduAn21j3japbymjcoGRGo5EQEoCMMhg//fRTWbJk/1oFuKZidtFvNrF27dpyyimn6FlHRE+17xk6dCgNxnQFsxxNlbJY9za1YZYjD8o3lHkonTPPFVn1tsie9e4Fl9r/UAbqnWonQxX8/GDd1yKL7lE7qj4g8BBkX66tcy3sIKDPwfWd/R2/O/9T4fehyqD609lv8pRIlb+pnQwvS0c8KnJQLWd/nTLQZp6n/o9WBweovVz2hMikVo6b4ZaZzrmDaojU6C1S73Z1EKK6Wu5oZ2Bm15rce1Nsmiwy52q1s1eJpqRIIyW/Ojer4yxq0+wozhhcoAEUH/SrBx/u7O/ZoOrbICUuyosQkpyMMhhHjhzp7jn07t3b11i0qVevnp5RtO9bvny5bNy40T0iaQfW4NVVCmNelB643CDSp1E6DXBDhKHY/mdlLA5UJ7JIsfID7odQsDCz1HKEE+gmm2jyrDL0/q6Mx1PcEylgZoUOf9BZuxeGsoT1h42V8VusjHO8bb4z07j0EXVQwIol3OWQRxRrKQHKJGZtO0wXaagM2eKuC3GYqHK+6oUPVvXOWr+dCkuUwo/fBe1ay/dEqvVQxxleDrfOcXcCAnd84y2AmTMajPEpUkykgdXvbZ6h/lBehJDkZJTBaAes6d69uzRtarmUJaBZs2ZSsqSbssFl69at7h4JJZuVkmk6wqKllEFwqqPYd5ztGIomZ1zWo5qAOrcoZfOD7JQJZnngggujMVVFu94dIiesFqmJGZ4QGIuGip2U0fi0M7NnWDo4f9baJaL0Ec7ax6oXOeWx5YeOQRUm2Xqpe6tIJ9WvHVTTPZECcNvd8K3TvqEMh2GwZ/sikZ9PctaXb5jgngxApTPUH1VOMFu74TvnXH4Az4Owpd7R64vdOoXAXzv+cPYJISQBGWUwLly4MOpKetRRyDsXjHnz5smuXfvXwxUtWlRq1LCUIZLeoFODq9qyIUpfDbjW5+ixTkqIViMdhaz5cEexD3PUTxsoTnBX2zhRKQRLldzirAdtOz58rn4k72CWv8MMZ5AFszdwVzbuu0FBipbv6oj82luVwQBpD+DS21YZQDBWK57gniRxwdpjGPAwFg/prPZDUId1hN0jnfXl8BLB+swggxTVe6o/7vfXM9R5HNhAMKvpZ4lMbqOMVxji+RjJtrBBrIBipd0Dxbbf1J8CHAgihISCjDIY9+7d6+6JlC5tNXgJWL9+vc7ZuG/f/gb/+uuvT+rKStIEBGP5SXXYS5TiCne1aac620SlxE4/Q2T1B+omn86uZDWRw9R1RCLMNEUKqR5WvqV2ctmJI2DJpNaOwjOjm1J62opMqCnyYxN17kyu8wnCqnccWWGmw6zxzEYwyHL0eJH2U0WqXqxOBKxLOiCQMvz2bRdZO0qVw3OzI5n/H8p4Q7lZlYf6GxS47B6p2kek1AnTgA8iDeP7oAzNuSp+G2+D9h6DG1iXjBnq3MoDwa+w7n1hf2fADeDZYZIvKNvC3QH79ao8E1HPQpA5QkjoKHaPwt0/4MAAfPLJJ2X27NnSqFGjHG6jXhD5dNKkSXr/0EMPjZs+wwbGIYLl2CAnY82auXABIgeO3etE5l2vDMYXnBlGA6I27lqpzrl549aq3xb36oiDIenUkQtv2WNONNftC1QnvMsZeS8SYHwHyhXShojPTCyUd8hs3VdKZmsd5SpsilB+gLI17XQnki7ktOknxz0OMx8HVXdvIgkpUtwxFHevcY73bhbZ+INIjT646JwLIwvvdtIVIAVIXtolrL2eeYHIiv9z2jy4CXufc5gqoyiTYZMnZsCQXslExUU5wvcs3UgdJPiu5dvkzrXcgIEh5KLdtco9oUAAIczghk3G6FMQ8Ayu0A0Hqa+Xx7kDzAjDC2juDaJzi2IdauXu6kLI5EZIFlMkUojhQhHl1ORURERT5FAsW7asezUnH330kZx//vlRt9QRI0bIOeec42s0wkgcNGiQTJgQuw7i5Zdf1rkYOcN4AFj1nrLyH3aUbkxmQ9kupZSBCu1FasOoSfAb/NIztVQHSDTf4h3RaSEyHUTfXPyg2rG+O9YplW+rvt9hSob1ReorxcYrPyhWv0IhV69DIIg9SQI7YQa2GXIIsi5EgSsvZngnIzWBx+iGEYS0L5mcOqOgwGwiohKjzCF/JxR8RDz+9Qp10SrHmAWqeZXaCan8UAfnXucMzgCsFyun2iYE2ioN4y4JGKzYPE0p3L8q4wURnF3ZYab38AfUThaVuyX/dZYhQAaoe43Ufl5mD+OBVByL7nXSchjKtxM5QhlSZZq7J0IIZgJhhJes7J7IBVgvirW0GLi163mNvsoQxZpntpOEhIVCNRh79eolr7/+etQAvOWWW3JENLXZuXOnXrs4d+5c94zIddddp41IzE7+9ddfsnbtWnnllVfkxx+txt8F+RrjpeEgBcD3hysFaJN74KHhI/FnGxYNdFy77A4oCAiv3gKJ+EPw+yKtwIpX1U4cGUB2kKH5rkgZMvEopagqhfOQk5Qc3nUC/6z9zIkcuHW2c5+XNmM87klZCoJtLBzgjLpD5giGg7Kr1/d4OEoZBdmW6y4emEWDgbR+rDpwyyoidjZQCjiU+7nKuLZdCsupMtr6K7UT4jYYivhvt6oytdA9oTjsNJFmr6udBN97QX+RVareYjYWFC+v6rXVfjZ/Q3TwrjDLzgsCLS17XO2o8oN1d8ctVvv5uJJm9Yci85QxH9ntHGOtbs1rM2NQA2uEIResNy7Xxjl3oFg/zjEUvYO6VS90ZFc2eIwJQkhmUKgG45w5c+Siiy6SWbNmuWdEXnvtNbn88svjGnVTp07VSfrtNYlBQO7Ffv360Vg8kExsKdE8dTaYDUS+N79ODuvvfkP+RatYYgS0ojIGMeoOd6Hdf7kXfGj+tlKquqidEPzOqz9S8lCdMgLXeMEsl1nrA/54xhklh9ww0+oNggG3yqWPxSr2oJ4yTOso5Rb34vVwp6vdT8kQaSayqK5M6aSMQzfxuaG9ksWCOx0XXltm1S4WaYSE/Vkkn3hMU4bQ5qnugQLr6jAzg/yCAMYTcjka+WGmvNNS7DjHYWWnavdgAMI1FeVE55VVW7wyg9QlyHtplzNEUF3qGksAAzttkBMzy8od6iWME5Qdu83LDzCLu/wltaNkXOs6kfp3q8cXd66lMzB0MVBjgvHAWwT9HpZvYJBh71b1XQY4MkuFX/s6/SxmCOMZzZhNxH3RsqrqcjVlKNa4moOPhISYQjUYAWYCO3XqFGMATpw4UTp06OAe5WTcuHFy4YUXypo17vqYBNx4441yySWXJHweKSAQknzlG457VpGDnLUp5Y923LTigYAD3tyJCOxQ+Vy143ZemNXACD7cv2wFC2BWA3nkwqRU/fWlM/MFV0m4pCJaZfVe6oL1HW3F/dj5zhogPxAMZ6cVRh0BM5piJlM9C0qAcS2qeYXI4f91zmcqcDXbMlt9hZJKkWkeX5nxugBjdrGGkq8J8oKZR6ylNdex7qcDZB1yoycZCJ70G4wgVy52WbL5vsH+WbOi6rfopNqFbJEd6mwypf1P1Ub+dovasdoyyBHynKz6rR2YVXNBDr1aN6idDK6XBwrk9Tyoas620guizVY41pn9ziRmXeDM9MUjkRePAQbmJtWWIT8jyt/Mvzn/QWvV7/gN6mIWHLOyRVWfDtli8NJOwUMICSWFbjCC559/XgenMR+lSpUq8tlnn8nRRyvFLQ67d++WUaNGyX//+1+ZPNmNZqY45JBDpHHjxnLppZfKeeedJ7Vq1XKvpA7ScWCd5EsvvaRTenz11Vdy8sknc5ayoEAwm4mt1I41e1znRpF6WMvjI3NE0FvzsdqxijDWTh2NTjSLlHmkzdBr7pTcDj5cpN0Paj/O9/fOCNlKPlKWIMIj1lABzAQ3VEZjJrlfQoGCgY2ZVNslMNHMlm0o+7k1Y4ZjCtI8WOUS98D11zDnGmdkHlF5kRMuLGkOEoFoxaaslGvtKJje74zBnR+xds+VXbLymW0gquQUZazAJdpgew8s/z8nEItp4+IZ5SSWX5Qho2d3ldwwU4a1s2GUGQLN/DnMCdBlQB8I1+X6cfpNgHqLID963aZbthqpZyHgmjmGlwnSUfk9AxGPsZbeTs9BCAk1adFrX3vttdrAM4bY6tWrpX379jJ+/Hh97EeJEiXk3HPPlfLly+vXnX766Trq6rp16/SsJdxPc2sswjC87LLL5Mgjj5T+/ftrYxGsWIH8TqTAWD9B/XE7K0Ptf6o/cTo9v9FPnWfRut/MbIQZBMowmKiUfqxX9cko+IYyzdwdBVyxmjzvKPUAM72/XB5rYKYzf6jPPutCVVGVkm0bi6BGb/UnTjnSLs5uuTOulDalGzsBh2z0mlCrrG783okUCOVt1kWO4b12pLrgKc9hAd4Dm2e4Bwq4sPmBVDi2DBDwKt7vkI0sfkCVVWsGEVS/TP1xZVShnfM/Hms+Efn5RGe2N6xlLQjzbxKZ0d3xPLEHdgBcTpdivXcI5VNHfe8O05WxN1QZxaqutVMG4NHfOsG54tUzGHswqBG1OCoTpQpi6QcGJMzr4NViUot4Qb9BY5GQrCJthnkR7KZ58/0RyeCietJJJ8nnn38enXn0Y8GCBfo6jMy8gGA5CIqD2cnTTjtNhg8fHvO+Tz/9tPTs2ZOziwUJ1s/ZwE2oWDn3wAe/fE8H13V3FHC3QSCYn5TShbWRYVWobHcgrF+Zp4xsr6G8dJDjwuSVQRWsL7PKNNJ32EYjZojsaI3pDFxOK6vvA6UHwRfguoe1sh2VgtQAASLi1N3dG9wdBQK2+OFd11SsjLvj0vQVZ52tYZMqy5i5nKg+U7zAT5kMgoMcZA3IbXLSHcWANbNeQ+YwZUjbICgToquGtW4mAwGp7O9e+ZzYQQvd/lnl1pv+AC6vSGEAQwmDJdoIyCIwWDZbGdhIQVTsIGdW8eeTROr9O7bOLh2i2kbVloWVapc6M6l+A15e0D+Y2AKlVH+J1CEdpjmzknrtuoVeP5+ldZMQEkPaGIzVqlWT999/X+rXr++ecTjzzDPlxRdf9DUa4Za6bNkyvf/nnz7BVQKwY8cO/XzMRsItdv78+e4VB0RuXbJkidxwww00FgsaJGq2KZUgVybcabzBSICOIuhSrKyTXmL7EmetFQJLZMpsWSrgO5Y+wj1QIOk8Zh1+7e2sSYHr4FJlOHllVa3HfsPQBmt5tNHo1kUYP+sQbCPNFYeKx4kc+YIy3oaJNH7GceurrmSANA+JsOu13wwtyuVGz0h7BayJtl4Ht92W74s0G66McGWY4/coWdXZEg16ZDK2DLAOD4GXkDNwhZI/ZjAwSGGXGbhaIlqoLTcYOoj2iDyXWYmnC65wjLvjYs9+azz3Y2AEroSQKdyxMcu22A1+lQ3MucLpB7A2vrlq99qMFx01tExTJ6BXtKztc9I8ZYtc4oF1/1v2BxnU6xzr3b5/0BEu9Xb9DGN/SQjJFWljMAIk7//kk0+kcuXYvEBwWUUKDmMcGrZvd3NdKWrXru3uBeedd97RbqdItYGUHTZnnXWWfP/99zJ48GCpW9eatSIFhzcYDjp4e/YBLpJIjD1JGTRQTr2dP5QEKFB2h4eZH2MUIQrh9LNElg1WByFTHBo9rjp9qw7AZRDKARRxrxsqQCLwI6y0HF5gNB750n7XIwTbiXdvpmMbPhsnKXn97OwbdC64vc4+gFIfL6feYco4b/KsSNsfRDrODndUSy03C0TZnajKy4J/ifz1mTph1TG4BPtFuDR5U5ECJhuV+dIN1B9LJrZ7OdDphSz8ArNgdqnZ/0SKu7PjyImJQaOwyxM5U01kWbhmArhV1v232lEyrarkYss2nntlNrHhW3dHgQBxh3rWWuslHRZF6XZKCHFIK4MRwC31iy++kNKlYxsq5GtEDkbbRdU2GKtWrRp4BhABdTp27CgXX3yxnj20qVOnjrz77rsycuRIOfbYY92z5IBQ61r1x/MbYo3PD41EJrdxIqguVwqUvcDfxm+RPxSs5m+q/24AJQR2QW6vBVAqQqRQYYYL+QERXt0rAxu4XNZVCn3LD9VtB7kn41C2lRNA6LilSn6t3ZMhpMJx7o4C7n0zzlPlra2zDnFi85wDDHqWjOgIiSaSbCKqXiDSELONPvfBBRrnETAoG9Hf3wIupgCBm+bfIjEJ0TGghllaPzkedrpIqxEih3QRHcW3DAbfkvwumQ5kZGRTEjNknu8L4xEz/AavMZSNmEEFAG8KbxeIvtE+iYHFRCB9DCEkK0g7gxG0adNGfvrpJ72G0Wb9+vXaRRXJ+uE6igA3Bq+B6WXbtm3ywQcfaCMQs4eTJsWuuSlXrpyO1jp37ly54IIL6H56INmz0d1R1EdEQI/s92xwZsziAdfTRkPc9Rc+vxuUMrgLVuqmDtzrcJvTM0feHjODOai6M9OA4Acw9uAWCVcjuKziPwIItZ+6fwTegOT0iz3BSbIJrBvTa+tcmUBpR+RZ5K5E3k8b5DqLp7SHCZQHO9VIPBo/6ZQn7+ADotLCiEFZhHtwPHkZt2fM6mLNcbZxsOVKDuA6/l0dkV+wLg+J/i35Iy9jonKH6JjIwYogKJmcOB1tfRBDxJ4tK2Wt4zYg8JVdf4se7O64YP3or30cV95swfYKwPrEJfc76z4X3iUyTfWfq99VF9wyh3Xa1S5RO3HK3IbvRCapfuanjuolnkBDhJDQkRZpNeKB9YUDBw6URx991HcNIyKhIhgNrsGtFEFrvIbenDlz5M0339TP8LqdGoYMGaJdXpGSgxxAoCDOvcHpsI76dH/6BnRey19UOwGKZuXuzqJ9O9pnIrDWCs/eNkek5jVKoU0QDCVbQBCEVW+LNFTKfY0r1IkslQfW0v2OHJ5xyh3cKuPNlIUFrNeEsWKU6KPHqLoVIBk3Xod1rpj9x8BFJRjgAcYjTU43yLziCc7ATraVv2T59ADWG2NQLKyywYDBmpGqL/jCMfQwCHgcIh0nKEO/qPpoXJ9hKHtT2Sz4j8gKpCBx6zMGN+wZcSxvWP682lHX0Q+gP8iGsocBCeRGToQehB3sBBGLJ5PZyphEncdgJAYivQGZCCGhIq0NRgPcUWHQJfqoCErz1FNPRQ3GCRMmyAsvvKCNxXive/DBB6VPnz5SvbpScMiBBUoBctdtmeHMRrT9zonYZoACBSNm9YfqwPr9cC/cZBBBFXnw4iVjTwYUE28Ajmxlxjmi83FhPQsCR2SzTDCrqGcmVjtrpBAsA2UMLrlIr+EFUT5RPrWBlOFyQ2RdBKsxAWhqXqEU6f+qnQL+XmgH1nykdpQcj50rUhzrZUMCXG2xtjoRWLc49zpn4Mxu6wDaOJQtBG/CmmQ77UEmg6UBf32l2h3V7mPdMNanR1GGBwJYtfxA7Sf4rr8P3T8LjgT1COBi7scsJdzKTYqNisfnfB4+w6+qjBu5Y+1xlb+r/RDINxGIKLv4Pjegkg9wfYaxmCz/7hTVDyNHLcp3m7FKbDQYCQkzGWEwghkzZuhopphF9PvILVq0kOnTp0vRokXloYcekrvuusv3vipVqsidd96p3U5pKBYSyFeH0WGTKw/J4RPNbCGqGxT4EhUdV6sixdwLWQjciLbMdpT5/FJspihlCr9JkFF9EsuMc5XipcomBjwyWW5Q2H/7j0RT2zR8WNVJ5FZMoYzB2EZ6DaQzSeV1SN2CFCQH1wvPLBqMIeT+g1zbfOO4iCcDeVIxgAZ3TKy/w+yOcdnF2lqki9BGzd/UiQyW0a6VIj8d6wxQGDBYeMiJroF8tjoR4PshrdJMzIC5/fwRgxzDevsiVZb/HeuyigT08ZYsGA+L4qp/6YgBTI/rahiB7JFqZKWSC9KNYI0/BsXKtwluNCPC8Z+u23Ttf4jUv1vth6DuEkJ8yRiD0QDDETOHWG9of3QEscFsIozKRx55JIexiBnI7t27S5cuXaRYsSw2ONIBJDZfP1btqN8IUU0bP63289DRRPY6I/RQGNDphxVE+ZsOZUrJDevG6t6m9vOhg0bUWRNIKJFiRXJi3N4QcRbKaibKDZEmkXIG5Qq5FeGel5uZLDPwAKVbByHJUhClFDM4kCfSFLT6RO3nsVxArlNgUJ0g0gLrzDK8fs4830mbVFYZKRXaB19S4GWyeu2Oxe6BAlF3d691D1xggCJadiKZLeiv6rG6B2vAs83zBDPcuUnCjzWMSNuEcg5ajXTKOyEklGTckHirVq3k2WeflalTp8q9994rxgUVifsbNGggDz/8cNRYbNKkiTYskaMRax1POeUUGouFDdJkGGMRQVmOQATKPHbO678VWTNC5A8Ynm7nFUaw3ssQL8F8brCTPa/GGrIsAe7OWEOblzJTsprzfzkU0gwteyUPEynf1lnD1frL4DM8NnAPhHsaDM2SWey5sfLtWGOx2WtqPx+ND7jqY2Yt04F7aCPVF8CVNLfGIkDeVdtV3GsswhUVaxeT/QaYUcdMMAI1ZZOxCHJjLAIsDUEgNSOvlcrYDnP/S0iWk7E+VEixce6550YNxkWLFun/hhtvvFF++OEHHQynWjVXqSOFC9aVLMaaKLdTqddflcAkqR2CYJKt65xcIQaGsVZEO6TuLpgIncPMfdZqdy1ZNrDiZfV9lRG+Kw+h4cu1cf5jBmg11khloOzgLnnUZyKHP6CMvSruyRQxwUXys1xmGnAnXajaNMgBAXyQzsdOY5AXMPNrgBthttTRZMCNEgFvdARsazAYgZcQzRiGabFy7skklG3p7mQICDQ1r5/It6rOLvWkwzhQ1L9r/3ISveabEBJWMnqxkncN4j//+U89k/jdd9/JE088wain6YZOtu8mQIdiaae5iAOi3OI33bIlQch9uKQCrHXc+ouzHzYQRXCHmzMU+e/yE4wU2zks18CFLuQKKXK4Yc0dUq6YWcLcgHVXJldZGGZ+cgPW1e5cIVK+newrb+W0zDawbm7vVselu+V7wQ2VIGB9MdJmAHgBbLfcMLMd5J2Ey+nxy5xctK2/EukwU6TBvepiSAcv9qwXmdndWXuJthrGY36DAZAggxOIQdD01cTpcwghGU9GG4zFixd39xwQyAZrFY87LouVlnQFAW7MLASiTsIFKEDnArdjDAS8/PLLvkGMNMUtxUyHpw+hsbNJGYwAbm4BgxIMGzZMrrzySp2/NCm1bxSpc4sygDo766TC3vEj3x3KSfXL1f88ftcjHnPcOWv3UwdZqDAhWIviq8m7VZtcQn788Ud9nFUgcM9mZaTAJRfrgHPZtU6bNk1HBB87dmzO9k5HrXTL11/KMApjO5cXipR0ZIRZxzCDvMUIGrdpqnOM6LD5HXAGHhNTTxWZf5MTcC4Z2hU9l94JhJCMIKMNRu96RKxjjGtUkMLFTgwPN5aANGvmrG+ZNGmS/u9LqXrujmKr6ujCSM2rnSA3R8DQCaYYIIcpDG0EggpUL+AijIAa+eVGl6789i/R0SuhWPpE9Pz555912zJgwIBgcsMsJdw5Dz7cPZFlYFa/SHEZNdUJOPXqq69mXzuMNcWdFos0HaYOcq+4jx8/XqeRQmC3HFQ+x91R7A4wCJRF/PbbbzJlihvh1w/kV0Xu3UwHEWaR/3DjD07+Q7jjYh1oHsocvHhyYNIFgX3bnP+EkKwmow1Gb5L+lStVY0rSE9MBwVj0JlhOQMuWzrqSr7/+Or4SWra5yGFuHjy4boUVREZFjqyAYLYddWTWrFnuGaJzkP2JQCSqLNW50TnnAel5UNa+/z5LXUxTpcFAkVYj5LRuiBIr8tJLL8mKFSv0flaBHLF5pG5dJxctBshytHdwfcbABFz5MzUibwGwefNmPbDYrl07HeAuB0j9sPh+J1F/ps/KYs0iXOmx3rKFassO6aJO5r4cPPPMM9K8eXOdwzqmvCFHpWH7UneHEJLNZLTBiJyLNr///ru7R9IORLPD7JgdVS0AlSpV0kbP2rVrZd8+NwmzH82GibT/ObCrazawZ4/T6Xtdt7OaVW+pP0oxQjoXM8jgYePGjfo/craSAGBmtXx7OeXUU6ODeN4gZCQY9erV0zJcsmSJ/PWXT2J1eBpgvV6pOu4JAo8A09aVLFlS/48BeQaBWeueyZRr6+ThRDCf0k3dk7ln/vz52lBctWqVe8YF72PY+Yf6k+GGNiEkz4RqhnHpUo6EpS1wp8rFqPiOHTt0h1a+fPkcAwQ5KFXb3SEARjaoXLmy/k8UVS4QOfTUhOsNzZpPDFaQ4NiBqSpUqODukVSoWrWquyeyYcMGd48kwngCdOvWTQ491MedPkzuu/X+I9LkBcmvfMNmcKxsWY9nTkXEgXDbR0Y/JYQoMi5xvw2MiTJlykRnnjp06KBTaSQ1LAqJyZMny9y5uV9jl+inSvYzZuJrwcyZM3XeTUS8feihh2IGCQrrc2XKa9944w09+n722WdL586dcwyw2BTU50pGQb1vXl47YsQIXVe7dOmiN6/cCutzpftroXzCxQ3HcIeuWLFiYq8AxYH4XH7k5bWgoN5706ZN0TWgffv2lXLlYiOtFtT7grz8VgX5uZK99uOPP5Y1a9boYHdHHulGknXB9cuPmS4nHrFUfllRRZ4YfYw651wrrO8L8vLsRJ871fdFRPk//vhDjj76aGnY0MrHqziv7WI5vcUf8vK4xjJ5cZWEz043WcI9+fbbb4/b52HdJnJ2o77lBtTLQYMGJU3ZdtNNNwWayDjssMN0ZP8chrtF0GeBnj17xqSdIyRfUJUtY1EGY0QZh2gt9KYUlMjevXvdq+mFMmRjPis3bty4cePGrWC34QPKRfaNqxT55KHyEaU/+97DLXwb9MN4vPLKK6osFPF9XdDt888/jyhD2X1iTmbOnJmSzjdhwgT3lTlJ9VmnnXZaws9GSG7I6BlG0KZNGx2K3IARI++obLpw1VVX+UYkSzQKlGy2NNFrk40uJXp2stcW1GcG9vWFCxfqCHg1a9aUFi1aFNp3Stf3TXR91KhRsn37dunUqZPUqFHDPbufwvpcBVmm8+O1I0eO1O68J554ojRo0ECfA+n4Gxfka1P9vlhDjtmeEiVKyDXXXJPr9072uQrrtaCg3xuB21577TU9a3LLLbdE1+Qlem1e6hMI8rniUdivhbzggQJ5YUapdOnSOV7bpf4EOabWzzJ3bUP5cM5Z6sXp3f74key1iUj02iFDhsjy5cvlsssuk9atc6YjKcjPXJDPbty4sZx88slx70N5gQdOXmYYL7/88qSfA+9h3H4TEeR5QZ8F8N0hA0Lyk4w3GOH69Nxzz0XdEhAswESaI5nPFVdcoV207rnnHp3mIFkDTRy2bdumOyG4CiEvXseOHd0rJBnHH3+8dtWC4h5EKSAOw4cP1/KCexuifCYzZEhOJkyYICeddJKut3v37qUMk4CoqLVq1dLywmBskyY+UaS3zhH55TKRyt1F6g9QJ1ifDQiyBDdHDJKdddZZbOsIIXHJ+N6oVatW7p7DunVuRDQSCkzkWzsYBEmOCXgDGPQmNTBDBkzkRRIM49kBrwCSO7Zu3aoHP6tXr+6eIYmwIxnniPRpKHOkE0E7v5Pbh4CDDz5Y/9+9e7f+Twgh8chog3Hx4sXaXdEGBmOGT5oSC+Rzw++JReEkOMhNZkDwERIcKOsYaV+2bJl7hgShadOmWm6IMotw/SR1jAIP44f9WHKKFSsWDXRDmaUOyhvq7K5du9wzhBDiT0YbjFdffbUMHjw4ppOAi+rUqVPdI5LpIPodSNd1qemKPTvGPIypgcio4M0336QCmgKIsnj44Yfr/Q8++ICyywUm7yxcLG0vARKfRo0aaZmtXr3aPUOCYgYoaDASQpKRsQYjgiuMHj1aKyUYZTTMmzdP2rZtK2PHjnXPkEzGrEkxrqkkGDQYcw/WMEIBhfcC1uKR4GDd5/3338+1n7nEzv1JAyg1aPSkTqlSpfR/uqQSQpKRsQbjAw88oI1FLHjv3r17DuUEuedmzZrlHpFMBZHb8NsicT8Jjm0kIlIqCQ5mLG6++WadE4vuvKlxzDHHyF133SV16tRxz5BUwFptRIQGcOvlLG1ykLAfMvPmYCTJ4QwjISQoGWkwvv766zohOejRo4ce0fZ2FogSeckll3CUNsNBMlvM8lx44YWcsUgBBIMaOnSoDsXN9Z+p89hjj+l1oFRCyYHGRKvcuXOne4Ykok+fPtoD5YwzzmAfkSKmb8hteglCSPaQcWk1sLYD+WUWLFigj6dMmaLDuINnnnlG+vXrFzMqe9ttt8mgQYPYkRBCCEl7MNg5ceJE6dy5M/stUqD89NNP8tZbb+m8qczbRwhJRMYZjGjcMKuIj418i4sWLYrJVYVRxi+//DLGaPz666+la9eu7HwJIYQQQgghJAUyziX1wQcfjBqDiIjqNQLvuOOOHOewHonruAghhBBCCCEkNTLKYHzvvffk119/dY9EzjzzzBzGISIcXnnllTHnZ8+erddzZdhkKiGEEEIIISTkINDZH3/84R6lHxnlkoq1iibHIgIDjBw50tfN9JdffpGWLVvq9Y42P/74o3Ts2NE9IoQQQgghhJDCY8SIEXL++edruwUxWkxO43QiY2YYP/roI5k2bZp7JHLZZZe5ezlp1qyZDBw4MIcxeeedd3KWkRBCCCGEkHxk3Lhxcu+991LPThFMcl1xxRXRSa65c+empQwzxmBEegVbgKeeeqrv7KLhqquuynF9zJgx8tJLL7EwE0IIIYQQkgLjx4+X++67z1ePRnDJsWPHukfhoiCNYcReWb9+vdSrV08f79ixQ/9PNzLCYPzuu+/0ZkAQm0MOOcQ98qd69ery7LPP5jAaET7apOQghBBCCCGEJAbGYpcuXbQHX+/evWOWfcGggjGFe/JqVKXbTCU+D773Pffck++fa/To0fLpp5/qZ5q88dWqVdP/042MMBiHDx8e8wPBzzfR7KLh6quv9l2zeO2118qWLVvcI0IIIYQQQkg8TjzxxOhkzf/+978Y4+nbb7/V/3FPEP08EZiphHFmjNDC5qSTTop+p/z+TG+88YZ+3iWXXKKzOdSsWVPbLXmVYUGQ9gbj4sWL5cUXX4z+QG3btpVjjjlG7ycDAn/ooYdyCB6uqbfccktaFERCCCGEEELSGbiirlu3zj1yjuGCWlC6NAzSdCM/ZlAN8HZ8/fXX9fOqVKmiz/Xp0yctjUWQ9gbjhx9+GPPjYNYwFWFiZKB///45XoO1jI8++iiNRhJKMNoHl2wMtnz99dcs50lYsmSJdnvHYBLcQ95++23dRmAUFR3EqlWr3DtJPDDy2qpVq5jgZISQ9GTNmjUyadIkef/99+Xxxx/XMx3Lly93rxISH7PWDpj1jMlm3tCPpsuMYbowatQoLQ9kgHjyySf1/gUXXBBjr8BNtXjx4lK3bl3Zu3eve7ZwSOu0Gjt37tTTs3/99Zd7RuT333+XWrVquUfBgJ91jx495J133slRWOE/3Llz57S16InIF198IV9++aWeFa5du7Z7lviBnKNwuf7+++/dMw433HCDDhyFhofEEi8Nj5ennnpKy5FtRU6gDKAdRfsKpbNGjRruFRKUOXPmyNq1a3XAA2zbtm3T/9EPQq7eDeW1dOnS0rdv36wrk1Cc0CdgVB5eRyQYiDaP8P0YUMQgmZeSJUvqwbGKFSu6ZwjZD/QH1L3BgwfLv/71r2ifCT26aNGiep0f2iYMvBo3TvQNOG/uvfvuu7W76cknn6xnJwcMGKCPTRsGo9I8B2sl/TIe2OD5J5xwQqA20DwXbrPJnuulWLFi0e+wZ88efZxXTjnlFC27G2+8UeeK79evnwwZMkTL0gbXO3TooN1WU/nM+Y4SXtry/vvvR5RwYOHp7ZprromoH8y9mhrr1q2LqEISfZbZWrRoEVEVwL2LpBuTJk2KqMqjf6v7778/179/tlCvXr0cZdxsr732GuXnw+LFiyNKQfKVmb0p5TSye/du91XE8Nlnn8W001deeSXLWQpMnTo1cvXVV8fIMJUNbWS2sHHjxsjzzz8fqVWrlv7u6NPZfwcDcjJ9qXcrVapUdP+LL75g/SU5uPfee6NtlDKYIsr4ih4royeijL/osTIYo2VIGVbRsmW2nj17xrR3dj22n9OrV6+YZ9kowzLSuXPn6L3KEI0owzPmXjzLHONe837e94wH3gPfG89VBnD0tfj+eWX58uU5ZDNjxoy0rntpbTB26tQpRpjxCk5QFi1alOOZ2ObPn+/eQdIJGPmtWrWK/k4XXnhhWlemdOCwww7Tsurfv39k2rRpkR9++CGqJNx6662UXxy2bNmiZYUO5pNPPomMGjVKK05DhgyJ6dgWLlzovoKAt99+Oyqf9u3bR+W0Y8cO9w6SiAceeCCmfCXbjjjiiMjZZ58d+ec//xl54oknIl9++WXW1Onff/89UqdOnagsLr744sgvv/ziXiVB+Pbbb/XA4YcffqjbOgyWbd68WcvR9BMoV+wniBdjMBpDC8aUKTM4B/3ctGVGV7eNTBh0Zt9rMMLgNGUO5c++hs2r+9vP9W62MYfPh88Gg8/vfvt9vdgGsXfLD4Pxo48+0p+vbt26+pmPPfZY2te7tDUYp0yZEi2M2Nq2bZsvI4lbt26N3HbbbTEFYdWqVe5Vkk7069cv5nc6/fTT075CFTZr1qyJzJkzxz2KRKZPn05FIBd89dVXkaOOOipa9rChw6P89vPCCy9E6+fAgQMjffr0iR6vXr3avYvEY/bs2ZEaNWpoeXXt2jXy+OOPR0aMGKFnbL/++uvI+PHj9SDGzz//rI2lXbt2ua/MTu644w5dvtCewfuIdTH/wMCDqbtPP/00ZUtyYGbDTD9oG4zwbLJnsNEf2Eaamf0zx4MHD47R743B6WcI4ppdHu17zOvsmUbbCMR74B77efbmZzB6Zy79tvwwGG0D+oQTTojs3LnTvZK+pK3BiM7T/sEwIpafjdjHH3+sZ1wwykbSj5deeilHhfU2HCQ59gwZlfhgfPPNNznK3nPPPceyZ4GZVtPhDxo0SMsGrqhGbhi4IIkxBlDTpk0jCxYscM8SPzATZsob62L+Y7tEZ5OLMwlG3759o+UDs4Nwz/T2kTAYjdunbaQZA9M29GCoeY0y4+ZqjrFh0NaeKPIalMZws41Xr8Fo7sUGQ9Z+X79BYNtN1BiksBPMd8OWaGYyKEamZcqU0YOHycCSPHsyoDBIW4PxhhtuiP6o+KHYQWQPcJsxFf3f//53tBxgFCY/ZpmziWOOOUbLLhPcHdKFSy65JFrmsD937lz3CjFghBgyOuuss6Llyp5hnDBhAj03kjBy5MiovLBBeZk3b557ldjYrrsc+MpfVq5cGe1vjzzySPaxJAbbGEu02QajvRmjznbxxLl4xp/XJTWewWgbbUENRjzL/hwwCOM933weg/0s7+tSZfv27VHD9Kmnnkqqmz355JP6/c3gbGGRtmk16tSp4+6J3HXXXe4eCTuIsNizZ08djQqRr6677rpoVCicI8FBVM+JEydK9erV5dJLLy3c6FoZRIsWLdw9kbfeekuaNGmiU2yo9tI9m92ojlJHyYM8lIIpvXv31hHxhg8fHpXR8ccfL1WrVtWR3RDtk+Tk7LPP1vXzmmuu0XUT4ekbN24szz//PMuaB2Uwapncf//9UqlSJV2m3n33Xbnjjjt05M/Nmze7d5JUQbRZU95Ql9lPkNxiIqMaEIlUGToxKTWUsaXvwTkbHOM6IoLiOQZzHpgUHniG/V5+93gxUVHvvvvuuGXcfCbcg89t8D7Tfr/cMGzYsOjrDzroIP3fD+i86GtvuukmvV+qVCn3SiGhPnRaAusd7nQIQFGYFjU5sFx00UXRER5EjMKIuxnZ4QxjcOy1iz/++KN7lgQFZQ/RGLFu1pRHrGtkWxTRM66mbAXZEA2OJAazsVgTWrx4cS2zBx98kGXNAhGKIRfUScxuw43LLmPmGmUWDCzxuf766/WynAYNGkRliNkdzHxTjsRgz95hrSLcUU0QGnu2zrhummNsRl+zZ+7gSeEXhMaeGbTvx2yeOW9m5ewZPnw+P/dWYM94wh0Vz/HOmPrNVHpnEP36Oz931qAgoCP0WXxmZSD76rXw0jn++ONjvheCzOX2PfODtDUYSfZhux19/vnnumIsXbo0WlkRGKIwK0sm0a1bNy3LTz/9lDLLI2Y97bPPPktZurz77ru6o0PY82uvvTby8MMPR/7zn/9E6y86U6wFpYtlamCgp2HDhlqGMCBZ3hxMdHO7jPltv/76q/sKkogePXoklCMUZ0JAPDdQYF8zRqTR14yB5jUWcc4Ymjj2e7bX8MSzvMFtYNTBeLXvMxue6113aD4fsA1dbPZ7+xml5jvhnHmN93Wp8uqrr0afa382RCy+6aabfL8XvlNu3y8/oMFI0gI7Ku6wYcOilWLTpk3R8wgnX5iVJVNA44rG5pVXXqG88ogd3AWNNYkP1pYZWb3++ussewHwS+mEADiQ49FHH+078pyNXHrppTEKFNIHIdr5Bx98EPnb3/4WvfbII4+w3AVk4sSJkauuuioqOxiR6DM4w0hsvGsPbezZOhhTKDfGSPMz6Mzr7Yir5noiY9Rs3uiq9oZneQ1KGGLm2DbKvLOMtnHovWZvuMfvGt7bfn4QkHrKpNRo3ry5DjzlnVHE9o9//CN6rrCjQ9NgJGnBrFmzIi1atIi88cYbOSqEyb115plnFmplyQSgqKNxYSTBvLNt27bIKaecouXZsWNHKu8BMGkiEOWa5S8xJkoeZrC9IdVN4CW4RpNY75Phw4fHyOv777+PKnFY0sByFxzk8zRyXbZsmXuWkP0kMhiBPSOHuued2TObMQhtg8w2GP2eDaMRRieuG6MOr8d5uLXifczso6n3uIbz5px5hrdd8Bqk9vub97Cvm+fh+8UzGr3vkQxMjsQzTitVqqQ9efDMdu3a6c9S2MELaTCStMfkY6xWrRqV9gRgXQrkhLW/hdmohAU7UjMi95LkdO/eXcusf//+LINJQMQ7U76QkH/AgAFa+bEVFUaadcA6WChNRpnCTBhyVtrpILAhhyXLXXBatmyp5dehQwf2rcQXYzDas3A29nVT9+w2DOe9s29el9DcGFv5gTEM480O4rqfG6jXmPT7jkGBl8QZZ5wRfd6FF16oDUk7GjQGFcuVK8e0GoQkww4/v3btWvcssXn55Ze1jKB03n777ZGhQ4dG3nrrLZ0AHG5v2Z70O1VM2giUOcixMDqzTAThvyE3zAhRZslB2wY3JKN4mA1BXZArmDLcz6JFiyKNGzfOISuzcc1n6hhF9dFHH6XsiC9mRjCRUYdZRttgTIZ5JuptYRmL+QG+R359dui2GzZscI/SkyL4o340QtKWPXv26BD969atE6U0SP369d0rBEAulStXTpp2RDXoOpT/rbfeGjesdLYyefJk+eabb6RGjRo6TL9S5DGYJg899JD079+f8grI7t27dcjwc889V5dJEgykNti6dauUKFFCSpYsKS1bttTpcEgsc+bMkeuvv17XV6TWQOqlCy64QC666CKWt1zw559/yk8//STdunVjG0dyDdJOoC5Cx0ilHCE9BV7HspcZ0GAkGcH8+fNl2bJl0rVrVzYuPkyYMEHnOYIStWHDBlm8eLHMmzdPlixZ4t6xn9WrV1O58tCjRw+dc9FuDu+5556EOZsIIYUHBsiKWrnSCCGEFBw0GAkJMTt37pRVq1bJypUr9daoUSOdiJ7EMmXKFHn22Wd1AvCKFStKr169pFOnTu5VQgghhJDshQYjIYQQQgghhBBf6M9BCCGEEEIIIcQXGoyEEEIIIYQQQnyhwUgIIYQQQgghxBcajIQQQgghhBBCfKHBSAghhBBCCCHEFxqMhBBCCCGEEEJ8ocFICCGEEEIIIcQXGoyEEEIIIYQQQnyhwUgIIYQQQgghxBcajIQQQgghhBBCfKHBSAghhBBCCCHEFxqMhBBCCCGEEEJ8ocFICCGEEEIIIcQXGoyEEEIIIYQQQnyhwUgIIYQQQgghxBcajIQQQgghhBBCfKHBSAghhBBCCCHEFxqMhBBCCCGEEEJ8ocFICCGEEEIIIcQXGoyEEEIIIYQQQnyhwUgIIYQQQgghxBcajIQQQgghhBBCfKHBSAghhBBCCCHEFxqMhBBCCCGEEEJ8ocFICCGEEEIIIcQXGoyEEEIIIYQQQnyhwUgIIYQQQgghxBcajIQQQgghhBBCfKHBSAghhBBCCCHEB5H/B9iV6zA+MBA7AAAAAElFTkSuQmCC"
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"
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"
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"
    }
   },
   "cell_type": "markdown",
   "id": "696327a6-fb70-44a7-ad76-4bc6131e6c9e",
   "metadata": {},
   "source": [
    "Die obige Identität kann man auf unterschiedlichen Wegen zeigen. Wir werden uns eine geometrische Lösung des Problems anschauen, die auf der Strahlungsintensität von Lichtquellen in der Physik beruht. \n",
    "\n",
    "\n",
    "Sei $l$ der Abstand zu einer Lichtquelle $L$ und an unserem Standpunkt eine Lichtintensität von $I$ messbar. Allgemein gilt der proportionale Zusammenhang $I \\sim \\frac{1}{l^2}$. \n",
    "\n",
    "In unserem Beispiel nehmen wir konkret die Messerte $I_1=1$, $l_1=1$ bezüglich einer Lichtquelle $L_1$ an. Dann folgt direkt, dass hier $I = \\frac{1}{d^2}$ gelten muss, d.h. unser Proportionalitätsfaktor beträgt genau $1$.\n",
    "\n",
    "Betrachten wir nun den Fall, dass hinter der Lichtquelle $L_1$ noch unendlich viele weitere identische (d.h. sie geben genau die gleiche Menge an Licht ab) Lichtquellen $L_2, L_3,\\dots$ in äquidistanten Abständen von jeweils $1$ Längeneinheiten verteilt stehen. D.h., $L_1$ steht nach wie vor $1$ Einheiten von uns entfernt, $L_2$ $2$ Einheiten, $L_3$ $3$ Einheiten, usw. und zwischen zwei benachbarten Lichtquellen beträgt der Abstand genau $1$ Längeneinheiten.<div>\n",
    " \n",
    "<div>\n",
    "<img src=\"attachment:31706f07-1b94-4817-9a4c-c7d69bf277ad.png\" width=\"600\"/>\n",
    "</div>\n",
    "    \n",
    "Insgesamt ist bei uns dann eine Lichtintensität von $I=\\sum_{i=k}^\\infty I_k = \\sum_{k=1}^\\infty \\frac{1}{k^2}$ messbar. <br>\n",
    "    Das entspricht genau der Summe aus dem Basler-Problem!\n",
    "    \n",
    "\n",
    "Spannen wir unser Beispiel nun einmal andersherum auf. <br>\n",
    "Angenommen, wir befinden uns auf dem Rand eines Kreises $K_1$ mit Umfang $U_1=2$ und Durchmesser $d_1=\\frac{U_1}{\\pi}=\\frac{2}{\\pi}$. Genau gegenüber von uns auf der Kreislinie befindet sich eine Lichtquelle $L^1_1$, von der wir eine Lichtintensität von $\\frac{1}{l^2}=\\frac{1}{d^2}=\\frac{\\pi^2}{4}$ messen. <br>\n",
    "    \n",
    "![image.png](attachment:5c46f921-279d-48c8-a6a6-499261e1035a.png)\n",
    "    \n",
    "Wir ändern unsere Konstruktion etwas ab, indem wir einen Kreis $K_2$ mit doppelt so großem Durchmesser $d_2=2\\cdot d_1$ betrachten. Wir legen eine Gerade durch den Mittelpunkt von $K_2$, die den Kreis $K_1$ nur genau dort schneidet, wo sich $L^1_1$ befindet. Wir erhalten genau eine horizontale Gerade $G_1$. Stellen wir nun an den beiden Schnittpunkten der Gerade $g^1_1$ mit dem größeren Kreis $K_2$ jeweils eine neue Lichtquelle $L^2_1$, $L^2_2$ auf, beträgt die Intensität an unserer Position $I_2=I(L^2_1)+I(L^2_1)= \\frac{1}{(\\sqrt{2}d_1)^2} + \\frac{1}{(\\sqrt{2}d_1)^2} = \\frac{\\pi^2}{4}$. \n",
    "\n",
    "![image.png](attachment:73a21884-bb38-4912-bcbf-44f04c4de8c6.png)\n",
    "    \n",
    "Wir setzen das Schema sukzessive fort: Wir verdoppeln wieder den Durchmesser unseres Kreises und nennen ihn $K_3$, betrachten alle Geraden $g^2_1, g^2_2$, die durch den neuen Kreismittelpunkt und genau eine Lichtquelle von $K_2$ gehen und stellen an jeden Schnittpunkt mit dem großen Kreis $K_3$ eine Lichtquelle. Auch hier beobachten wir durch eine analoge Rechnung: Die Lichtintensität $I_3$ bleibt gleich.\n",
    "    \n",
    "![image.png](attachment:cee63aff-b96a-4203-84af-2abbc3131aff.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3999c2c-61a8-4792-8466-84a3e6555501",
   "metadata": {},
   "source": [
    "Hier sind ein paar wichtige und hilfreiche Formeln nochmal aufgelistet.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Strahlungsintensität</b> <br>\n",
    "$I \\ \\hat{=}$ Intensität der Lichtquelle (in $W\\cdot m^{-2}$)<br>\n",
    "$l \\ \\hat{=}$ Abstand des Messpunkts zur Lichtquelle (in $m$)<br>\n",
    "    $$I \\sim \\frac{1}{l^2}$$\n",
    "Bzw. speziell bei uns mit Proportionalitätsfaktor $1$: $I = \\frac{1}{l^2}$\n",
    "\n",
    "    \n",
    "    \n",
    "<b>Inverser Satz des Pythagoras</b> <br>\n",
    "In einem rechtwinkligen Dreieck mit Katheten $a,b$ und Höhe $h$ gilt $$\\frac{1}{a^2}+\\frac{1}{b^2}= \\frac{1}{h^2}$$\n",
    "</div>"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "485c590f-0131-4b18-b3f0-b725967d48bd",
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    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Machen Sie Sich klar, dass man dieses Prinzip beliebig oft auf immer größer werdende Kreise anwenden kann, ohne dass sich die insgesamte Lichtintensität ändert. Schreiben Sie dies formal sauber in einem Beweis auf: Zeigen Sie für allgemeine $n\\in\\mathbb{N}$ durch vollständige Induktion, dass $I_n=\\frac{\\pi^2}{4}$.\n",
    "2. Beweisen Sie, dass die Lichtquellen entsprechend der obigen Konstruktion auf dem Kreisbogen von $K_n$ in äquidistanten Abständen verteilt sind. <br> Genauer: Zeigen Sie, dass auf dem Kreis $K_n$ die Lichtquellen $L^n_j, j=1,\\dots,2^{n-1}$ auf dem Kreisbogen gemessen genau einen Abstand von $2j-1$ zum Standpunkt des Beobachters haben. <br>\n",
    "    (<i>Hinweis:</i> Das bedeutet gerade, dass $K_i$ für $i\\to\\infty$ gegen die erste Konstruktion aus Grafik 1 konvergiert, mit der kleinen Abänderung, dass jede zweite Lichtquelle $L_2,L_4,L_6\\dots$ abgeschaltet wird. Also so: \n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:a48dccf8-1d86-4e3e-ba1c-be8e92cb01c2.png\" width=\"500\"/>\n",
    "</div>)\n",
    "    \n",
    "3. Zeigen Sie, dass $\\sum\\limits_{n=1}^{\\infty} \\frac{1}{n^2} = \\frac{4}{3}\\cdot \\sum_{n=1}^{\\infty}\\frac{1}{(2n-1)^2}$\n",
    "    \n",
    "4. Zeigen Sie unter Verwendung der obigen Teilaufgaben, dass Eulers Behauptung $\\sum\\limits_{n=1}^\\infty \\dfrac{1}{n^2} = \\dfrac{\\pi^2}{6}$ wirklich gilt.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86c1e21e-cfa9-4a74-9468-a6837cf929dc",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63afb5bb-b759-4e6c-ba8d-76e4d502c719",
   "metadata": {},
   "source": [
    "### (Unnützes) Wissen über π\n",
    "\n",
    "- Das Verhältnis von Umfang zu Höhe der Pyramide von Gizeh beträgt etwa π.\n",
    "\n",
    "- Es heißt, dass Pythagoras eine große Angst vor irrationalen Zahlen hatte, also insbesondere vor π.\n",
    "\n",
    "- Bisher wurde Pi auf 100 Billionen Stellen genau berechnet, was 157 Tage dauerte.\n",
    "\n",
    "- Es gibt einen internationalen Feiertag, an dem man die Zahl Pi feiert. Der offizielle <i>Pi Day</i> ist aufgrund der amerikanischen Daten-Schreibweise der 14. März (3/14). An diesem Tag wird traditionell ein runder Kuchen (Englisch: <i>pie</i>) gebacken und gegessen.\n",
    "\n",
    "- Albert Einstein wurde am Pi Day 1879 geboren.\n",
    "\n",
    "- Der aktuelle Rekord im <i>Pi-Sport</i>, bei dem das Ziel ist, möglichst viele Nachkommastellen der Zahl auswendig aufsagen zu können, liegt bei 70.030 Nachkommastellen. \n",
    "\n",
    "- Die Sprache <i>Pi-lish</i> ist auch allein der Zahl Pi gewidmet. Hier entspricht die Länge des $n$-te Worts genau der $n$-ten Nachkommastelle von π. Es wurde sogar ein ganzes Buch auf Pi-lish geschrieben."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "060c8726-9c7b-4201-8e25-b550768f9280",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2a00191-4ecf-4013-913a-525d68b79669",
   "metadata": {},
   "source": [
    "Überraschenderweise tritt π total unerwartet in allen möglichen Lebenssituationen auf, auch wenn sie auf den ersten Blick nichts mit Kreisen zu tun haben. Das stellte auch der Mathematiker Georges Louis Leclerc de Buffon im Jahr 1733 verblüfft fest. Dieser beschäftigte sich mit der folgenden Frage:\n",
    "> <i> Wenn man eine Nadel der Länge $l$ auf eine Dielenboden mit gleichmäßigem Fugenabstand $d>l$ zufällig fallen lässt, wie groß ist die Wahrscheinlichkeit, dass die Nadel eine Fuge zwischen den Dielen kreuzt? </i>\n",
    "\n",
    "Dieses Problem ist auch als das Buffonsche Nadelproblem bekannt. <br>\n"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "dcc71126-877d-44b1-b067-972ec0b4d99f",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "![image.png](attachment:22c4b746-77c1-451c-878a-dafb638925d0.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "837bc104-e5d6-4b6f-8d51-89721e6604e7",
   "metadata": {},
   "source": [
    "\n",
    "Spoiler: Die gesuchte Wahrscheinlichkeit beträgt $p=\\dfrac{2\\cdot l}{\\pi \\cdot d}$. \n",
    "\n",
    "Das glauben Sie nicht? Dann rechnen Sie einfach selbst nach!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac98d17e-f014-4541-a0ac-1036bd6a1fef",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "1. Schaffen Sie Sich eine geeignete Arbeitsumgebung und führen Sie das obige Wahrscheinlichkeitsexperiment für $N=50$ aus. Wie gut sind Ihre Annäherungen an den exakten Wert von π?\n",
    "    \n",
    "2. Für bessere Annäherungen braucht man immer größere $N$, was sich in der Praxis als schwierig erweist. Nutzen Sie die Julia-Methode <code>rand</code> ([hier](https://docs.julialang.org/en/v1/stdlib/Random/) geht's zur Dokumentation), um das Zufallsexperiment für beliebige $N\\in \\mathbb{N}$ zu simulieren und führen Sie mehrere Experimente durch. Wie groß muss $N$ sein, damit Sie eine Annäherung von π mit einer Exaktheit von 10 Nachkommastellen erhalten? Visualisieren Sie Ihre Ergebnisse durch Plots.\n",
    "    \n",
    "3. Finden Sie nun einen exakten Beweis für die Vermutung, dass $p=\\dfrac{2\\cdot l}{\\pi \\cdot d}$ und veranschaulichen Sie Ihre Rechnungen.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "672f6adb-9ed4-4a16-bf11-28b27a0afdfe",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ac27a1e-e534-41e0-befe-0d8eb959e4c0",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Eine Zahl $z\\in\\mathbb{R}$ heißt <b>irrational</b> genau dann, wenn sie sich nicht als Bruch zweier ganzer Zahlen darstellen lässt, d.h. wenn $z\\in\\mathbb{R}\\setminus\\mathbb{Q}$.    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50e7c1d8-afc7-4503-b50e-2c57d64ff5e9",
   "metadata": {},
   "source": [
    "Dass π zu den irrationalen Zahlen zählt, weiß man seit den 1760er Jahren, als Mathematiker Johann Heinrich Lambert erstmals einen Beweis für diese wichtige Eigenschaft der Kreiszahl lieferte. Damit wurde endgültig die altertümliche Auffassung, dass sich eine solch fundamental wichtige Naturkonstante durch einen einfachen Ausdruck darstellen lassen müsste, beseitigt. Gleichzeitig vermutete er eine weitere Eigenschaft: Lambert stellte die These auf, dass π eine transzendente Zahl ist. Beweisen konnte er seine These aber noch nicht."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97948d81-7268-414f-be62-2b8c2bda2c0a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Eine Zahl $z\\in\\mathbb{C}$ heißt <b>algebraisch</b> (über $\\mathbb{Q}$), wenn sie Nullstelle eines Polynoms $p\\in\\mathbb{Q}[x]$ mit $deg(p) >0$ ist.\n",
    "    \n",
    "Eine Zahl $z\\in\\mathbb{C}$, die nicht algebraisch ist, nennt man <b>transzendent</b>.    \n",
    "    \n",
    "Die Menge aller algebraischen Zahlen nennt man <b>algebraischer Abschluss</b> $\\bar{\\mathbb{Q}}$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35de6217-f74d-44e5-89ce-ee0cbbb9b60b",
   "metadata": {},
   "source": [
    "Den Beweis für die Transzendenz von Pi brachte 1882 Carl Louis Ferdinand von Lindemann. Dieser war im Vergleich zum Beweis der Irrationalität deutlich komplexer, da er auf Erkenntnissen in der Zahlentheorie beruhte, die erst wenige Jahre zuvor bewiesen wurden. \n",
    "Beispielsweise verwendete Lindemann die <b>Eulersche Identität</b>, die besagt, dass $e^{i\\pi}=1$ und die Tatsache, dass die Eulersche Zahl $e$ transzendent ist.\n",
    "Eine große Rolle spielt außerdem der Satz von Lindemann-Weierstraß, welcher bis heute eine wichtige Rolle in der transzendenten Zahlentheorie spielt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8de1fdcc-b8ed-4b13-8065-0adb93b9f4df",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Satz von Lindemann-Weierstraß</b>\n",
    "    \n",
    "Seien $\\alpha_1,\\dots,\\alpha_n$ paarweise unterschiedliche algebraische Zahlen (über $\\mathbb{Q}$). Dann sind $e^{\\alpha_1},\\dots,e^{\\alpha_n}$ linear unabhängig, d.h. für alle $\\lambda_i\\in \\bar{\\mathbb{Q}}$ gilt: \n",
    "    \n",
    "$$\\sum\\limits_{i=1}^n \\lambda_i\\cdot e^{\\alpha_i} = 0 \\quad \\Rightarrow \\quad \\lambda_1=\\dots=\\lambda_n=0$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27e4cf5f-57bc-42fb-8e1c-d10e4b95b33c",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "Beweisen Sie mit Hilfe des Satz von Lindemann-Weierstraß und den Informationen im obigen Abschnitt, dass π transzendent ist.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f65da6-a41d-466c-a2d7-c0416cf45ab6",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63961a41-ed4d-4312-95ad-a2685f1ab580",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    \n",
    "### Aufgabe\n",
    "***\n",
    "\n",
    "Backen Sie einen traditionellen Pie zu Ehren von π und dokumentieren Sie diese kulinarisch-mathematische Erfahrung in Form von Fotos. Sie dürfen auch eine Kostprobe mit zum Seminarvortrag bringen.   \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46c10719-bef7-4559-a5c0-ddfd271c38c3",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f072f71-169e-4391-a2bc-fb752d4647a9",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "### Rückblick-Aufgabe\n",
    "***\n",
    "Das Ziel dieses Projekts war es, einige spezielle Wege aufzuzeigen, wie man sich der Kreiszahl π annähern kann. Wir haben gesehen, dass π nicht nur bei Kreisen auftritt, sondern auch in vielen verschiedenen anderen Situationen, die auf den ersten Blick gar nichts mit der Konstruktion von Kreisen zutun haben: π findet sich scheinbar fast überall in der Natur wieder. \n",
    "    \n",
    "Welches der im Notebook vorgestellten Zusammenhänge mit der Kreiszahl finden Sie am interessantesten? Warum?\n",
    "    \n",
    "Finden Sie weitere Beispiele für Situationen, in denen man dieser Zahl begegnet und die weitere Möglichkeiten und Formeln eröffnet haben, wie man die Kreiszahl π berechnen kann. Suchen Sie Sich ein Ergebnis aus und beweisen Sie dieses formal (eine Andeutung des Beweises/Bewisskizze reicht aus, falls der gesamte Beweis zu umfangreich ist).\n",
    "    \n",
    "</div>"
   ]
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    "***"
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    "### Literaturhinweise\n",
    "- Pi. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Pi\n",
    "- Inverse Pythagorean theorem. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Inverse_Pythagorean_theorem\n",
    "- Basel Problem. (2023). In <i>Wikipedia, The Free Encyclopedia.</i> https://en.wikipedia.org/wiki/Basel_problem\n",
    "- Martin Aigner, Günter M. Ziegler (2013): <i>Das BUCH der Beweise.</i> Heidelberg: Springer Berlin."
   ]
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