If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.
Gauss's Double Point Theorem
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References
Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 61-66, 1957.Referenced on Wolfram|Alpha
Gauss's Double Point TheoremCite this as:
Weisstein, Eric W. "Gauss's Double Point Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssDoublePointTheorem.html