diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..e558161
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,1034 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.8.5"
+manifest_format = "2.0"
+project_hash = "b78e0180f969db2968b2929877e28aee18cb3bd2"
+
+[[deps.ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+version = "1.1.1"
+
+[[deps.ArrayInterfaceCore]]
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+git-tree-sha1 = "e5f08b5689b1aad068e01751889f2f615c7db36d"
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+version = "0.1.29"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[deps.Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[deps.BitFlags]]
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+uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
+version = "0.1.7"
+
+[[deps.Bzip2_jll]]
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+
+[[deps.Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
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+
+[[deps.ChainRulesCore]]
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+[[deps.ColorSchemes]]
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+[[deps.ColorTypes]]
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+[[deps.ColorVectorSpace]]
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+[[deps.ConstructionBase]]
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diff --git a/Project.toml b/Project.toml
new file mode 100644
index 0000000..20b248e
--- /dev/null
+++ b/Project.toml
@@ -0,0 +1,3 @@
+[deps]
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
diff --git a/Untitled-1.ipynb b/Untitled-1.ipynb
deleted file mode 100644
index a0b86f8..0000000
--- a/Untitled-1.ipynb
+++ /dev/null
@@ -1,155 +0,0 @@
-{
- "cells": [
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#vdP.ipynb\n",
-    "\n",
-    "by Hezy Amiel\n",
-    "\n",
-    "find the sheet resistance Rs from R1 = R_AB,CD and R2 = R_BC,AD\n",
-    "the solution is from the equation in a paper by L. J. van der Pauw:\n",
-    "\"A method of measuring the resistivity and hall coefficients of Lamellae of arbitrary shape\", Philips Technical Review, Vol 26, 220."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "from scipy import optimize\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# define the equation\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def fun(Rs):\n",
-    "    return np.exp(-np.pi*R1/Rs) + np.exp(-np.pi*R2/Rs) - 1\n"
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# these are the resistance R_AB,CD and R_BC,AD respectivly\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "R1 = 65\n",
-    "R2 = 89"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_10913/3449932788.py:2: RuntimeWarning: divide by zero encountered in divide\n",
-      "  return np.exp(-np.pi*R1/Rs) + np.exp(-np.pi*R2/Rs) - 1\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# plot the fuction\n",
-    "Rs = np.linspace(0, 10*np.sqrt(R1*R2), 200)\n",
-    "# Rs = np.linspace(0, 10000, 200)\n",
-    "plt.plot(Rs, fun(Rs))\n",
-    "plt.axhline(color=\"r\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " message: The solution converged.\n",
-      " success: True\n",
-      "  status: 1\n",
-      "     fun: [ 0.000e+00]\n",
-      "       x: [ 3.460e+02]\n",
-      "    nfev: 13\n",
-      "    fjac: [[ 1.000e+00]]\n",
-      "       r: [ 1.986e-03]\n",
-      "     qtf: [-8.251e-12]\n"
-     ]
-    }
-   ],
-   "source": [
-    "\n",
-    "# find the solution\n",
-    "root = optimize.root(fun, [1])\n",
-    "\n",
-    "print(root)"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "base",
-   "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": "3.10.8"
-  },
-  "orig_nbformat": 4,
-  "vscode": {
-   "interpreter": {
-    "hash": "e7dcbe0a3ba33df212a58217d5216c6b91e63efd6156f57d0c8ac9d14a3fc559"
-   }
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}