This exercise is intended to refresh the student in continuous mathematics, which is important in graphics and simulation:
A slightly crooked wealthy man (SCrWM) orders a new pool table for his house. He wants it professionally installed so that it is level and does not wobble, so he creates a contract with the seller so that he will not have to pay for the table until it is shown to be "level in all directions."
After the table is installed the installer demonstrates its levelness by placing an accurate spirit level on the table in the north-south direction and asking the buyer to observe that the bubble is centered in the marks. Then the installer rotates the level to the east-west direction and again asks the SCrWM to observe it is level in that direction. Having demonstrated this, the installer asks for payment.
At this point, the SCrWM says "I don't have to pay you. The contract clearly states that the table must be shown level in 'all directions.' You have only shown it to be level in two. There are an infinite number of different directions in the plane of the table, and it will take you an infinite amount of time to measure levelness in all of them. You may stay for a day, a week, a year, I don't care, but I will never have to pay you. You might as well leave now."
But the installer is too clever for this tactic to work. He says "But any fool can see that demonstrating the table level in two directions also demonstrates its levelness in all directions. Allow me to prove it to you." And he does so. After the proof, the SCrWM says "Here is your money. Your proof is irrefutable."
Students: prove that two orthogonal measurements are sufficient. That is, show that if the spirit level bubble is centered both north-south and east-west, that it will also be centered for northwest-southeast and all other directions.