Quantum theory and the division by zero

Background:Division by zero is undefined in arithmetic, and the quotient 0/0 is an indeterminate form. In geometry, the same quotient appears when a side of a right triangle vanishes.Material and methods:The right triangle is described by positive self-adjoint operators for two observers, one at rest with the system and one external. The Pythagorean theorem is used in its normalised form, together with the negation operator and the commutator of the hypotenuses of the two observers.Results:A relation between the squares of the sides follows from the Pythagorean theorem. If one leg vanishes, this relation gives 0/0=1. The condition is that numerator and denominator are the same quantity.Conclusion:In the operator description of the right triangle, the Pythagorean theorem leads to 0/0=1. Whether this is generally valid remains to be examined.