I learned in high school what geometers discovered long ago:
[[Geometer, holding a compass and straightedge, looks sad.]]
Using only a compass and straightedge, it's impossible to construct friends.
{{Title text: The Greeks long suspected this, but it wasn't until April 12th of 1882 that Ferdinand von Lindemann conclusively proved it when he constructed himself the most awesome birthday party possible and nobody showed up.}}
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