newton-raphson--tusi-for PI.ipynb

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    "## PI day, March 2023\n",
    "### Newton_Raphson_Tusi algorithm\n",
    "Find $x$ such that $cos(x)=0$ around $x_0=1$; then $\\pi=2x$\n",
    "##### Author: Hamed Shah-Hosseini, Twitter:@chekaad, Instagram: @ostad.ai\n",
    "https://github.com/ostad-ai/PI-estimation-methods"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "from math import cos,pi"
   ]
  },
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   "source": [
    "def diff_x(f,x,dx=.0001):\n",
    "    return (f(x+dx)-f(x))/dx\n",
    "\n",
    "def newton_raphson_tusi(f,x0,n_iter=100):\n",
    "    x=x0\n",
    "    for i in range(n_iter):\n",
    "        x-=f(x)/diff_x(f,x)\n",
    "    return x, f(x)"
   ]
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   "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated pi: 3.141592653589793\n",
      "pi of math:   3.141592653589793\n"
     ]
    }
   ],
   "source": [
    "pi2,f_eval=newton_raphson_tusi(cos,1)\n",
    "print('Estimated pi:',2*pi2)\n",
    "print('pi of math:  ',pi)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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