“You must teach my son about triangles!” cried the Emperor, lifting his eyes for the first time from the bowl and the unicorn horn and staring wildly at the astronomer. “The relations of their sides, the relations of their inner angles and their outer ones!”

The Chamberlain said: “Matthias will ask, How far is the New Star? And the Prince will proceed calmly to his scientific cabinet, procure from within it one of your state-of-the-art tubes, aim it at the star, and then perform for the Electors a dazzling calculation of its remoteness based upon the principles of trigonometry you shall have taught him. And since mathematical reason is or is regarded as the queen of reason, his sanity will be demonstrated beyond all doubt.” The Emperor whispered into the ear of the Chamberlain, and the Chamberlain said: “You must go into his turret and teach him all about triangles!” And the Emperor whispered in his ear again, and the Chamberlain said: “All about all triangles. How the sides relate to the sides and the angles to the angles, and the sides to the angles and the angles to the sides.” The Emperor whispered in the Chamberlain’s ear and the Chamberlain said: “This cannot be done through the door of the turret, it must be done in the turret, inside the turret, face-to-face interaction is vital for truly teaching someone trigonometry.” The Emperor, gazing at the bowl, murmured: “For Pythagoras, the triangle lay at the root of all things, beneath the circle, beneath the square. For Pythagoras the square was really nothing but two right triangles, pressed together. When you see a square, you are actually seeing triangles, two of them, pressed tightly together, the diagonal line of their union erased, Pythagoras taught, and for this he was killed.”

The Chamberlain said: “Now, Matthias and the Electors depart from Frankfurt this afternoon. They will arrive in Prague in a week. Between now and the moment at which they cross the Old Stone Bridge, you shall teach the Prince enough trigonometry for him to produce a reasonable estimate of the distance of the New Star.”

And the astronomer, who by now had concocted a ploy of his own, replied: “It cannot be done.”