## Angle of Opportunity

My wife and I noticed that one of our sons has been getting his pants wet while urinating. He’s 8; these things happen. But when it occurred twice on consecutive days, we had reason for concern. When we inquired, he explained, “Sometimes when I start to pee, I hit the back of the seat. So I push my penis down, but then I hit the front of the toilet, and the pee ricochets and gets my pants wet.”

My wife began to pursue a line of investigative questioning, but I stopped her. “This is just simple geometry,” I explained.

I could have predicted my wife’s reaction. She said:

Not everything has to be a math problem. Especially this.

Even if that were true (it’s not), this situation still begs for some trigonometric analysis.

I’m just over 6 feet tall, so my fire hose is approximately 20″ above the toilet when I urinate. As shown in Figure A, when I stand a reasonable horizontal distance from the commode, my angle of opportunity is approximately 30°.

Figure A.

My son, on the other hand, barely clears 4 feet. His water gun is less than 6″ above the toilet when he urinates, so his angle of opportunity is a mere 20°, as illustrated in Figure B.

The images clearly indicate why mothers tell their sons (and husbands), “Stand closer to the toilet when you go!” Doing so increases the angle of opportunity and thus decreases the likelihood of a “clean-up in Aisle 3.”

But more importantly, the above images and some quick trig calculations show that an adult male — who probably has greater control than a young boy, anyway — also has a 50% greater range through which to aim when making a deposit.

Upon completing my explanation, I turned to my son. “Though it may be harder for you to hit the mark, that doesn’t excuse peeing on your pants. I think you need to be more careful.”

I then addressed my wife. “I also think we need to cut him a little slack on this one.”

“And I think,” she said, “that you are absolutely unbelievable.”

With that, she excused herself.

I’m not sure where she went, but I suspect it was to text one of her friends about how lucky she was: not only is her husband good at math, but he can apply it in extremely esoteric situations.

Rather remarkably, there has actually been serious scientific investigation into this phenomenon:

More importantly, there are a number of jokes at the intersection of math and urination:

Why do statisticians choose the last urinal?
Because there’s only a 50% change of being splashed by someone else.

What’s in the toilet of the math department restroom?
A natural log.

What does a mathematician call a toilet seat?
An ass-toroid.

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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