Allow me to propose a thought experiment.  Suppose you, and you alone, were to make first contact with an alien species.  Since your survival and the survival of the entire human race may depend on the extraterrestrials recognizing you as a member of a rational species, how would you convey your knowledge of mathematics, logic, and the scientific method to them using only your personal knowledge and whatever tools you might reasonably have on your person on an average day?

When I thought of this question, the two methods that immediately came to mind were the Pythagorean Theorem and prime number sequences.  For instance, I could draw a rough right triangle and label one side with three dots, the other with four, and the hypotenuse with five.  However, I realized that these are fairly primitive maths.  After all, the ancient Greeks knew of them, and yet had no concept of the scientific method.  Would these likely be sufficient, and if not what would be?  Could you make a rough sketch of the first few atoms on the periodic table or other such universal phenomena so that it would be generally recognizable? Could you convey a proof of rationality in a manner that even aliens who cannot hear human vocalizations, or see in a completely different part of the EM spectrum?  Is it even in principle possible to express rationality without a common linguistic grounding?

In other words, what is the most rational thought you could convey without the benefit of common language, culture, psychology, or biology, and how would you do it?

Bonus point: Could you convey Bayes' theorem to said ET?