Github #246 Pi computed incorrectly
I incorrectly used area * pts/N to comput pi,which happens to work if radius = 1, but fails otherwise.
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Roger Labbe committed
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@@ -542,8 +542,10 @@
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]
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},
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{
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"cell_type": "markdown",
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"The result of the multiplication is taller and narrow than the original Gaussian but the mean is unchanged. Does this match your intuition?\n",
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"\n",
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@@ -36,7 +36,7 @@
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" <style>\n",
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" .output_wrapper, .output {\n",
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" height:auto !important;\n",
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" max-height:10000px; \n",
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" max-height:100000px; \n",
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" }\n",
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" .output_scroll {\n",
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" box-shadow:none !important;\n",
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@@ -111,7 +111,7 @@
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"image/png": "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 truncated
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"text/plain": [
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"<Figure size 900x400 with 2 Axes>"
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]
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@@ -287,7 +287,7 @@
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"from numpy.random import uniform \n",
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"\n",
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"N = 20000 # number of points\n",
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"radius = 1\n",
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"radius = 1.\n",
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"area = (2*radius)**2\n",
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"\n",
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"pts = uniform(-1, 1, (N, 2))\n",
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@@ -297,7 +297,7 @@
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"in_circle = dist <= 1\n",
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"\n",
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"pts_in_circle = np.count_nonzero(in_circle)\n",
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"pi = area * (pts_in_circle / N)\n",
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"pi = 4 * (pts_in_circle / N)\n",
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"\n",
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"# plot results\n",
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"plt.scatter(pts[in_circle,0], pts[in_circle,1], \n",
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