I’m a student. I don’t understand your calculations. How did you get the area, the radios and the angle?

Thanks!

On that note, anyone willing to help/discuss elementary ed? I’m teaching all subjects, and the math is interesting in the new books we have. One student was disturbed that she received a wrong mark for adding the equals sign and the answer when the problem asked for the numerical or algebraic expression (4th grade). We’re actually spending a lot of time and 2 or 3 chapters on these expressions which involve very easy operations. Does anyone have a comment on how/whether this helps with future word problem solving in Alg. 1 or 2?

In that case, the larger button would probably be pushed the most because it’s easier, and should be the lower-gallon flush, and the smaller button should be for the double flush.

I remember that they discussed how the toilet works after that segment. I’m pretty sure that there are two valves on the toilet to make it flush. The 0.9 gallon button opens one valve, and the 1.6 gallon button works both. I am going from memory, so don’t hold me to those details.

That said, I want to agree with Scott. Maybe that makes me a bit of a killjoy. What’s the best design? The best design is one that works well for people: e.g., is easy for people to understand, is easy to use, is natural and intuitive. Thus I suspect the best design has one button noticeably larger than the other (so it’s easy to intuit that one causes a larger flush than the other, and easy to guess which one causes a larger flush), yet is chosen so neither button is too small (to make both buttons easy to press for those). I too think the toilet manufacturer nailed it.

Anyway, I’m classifying this primarily as a design and human factors challenge, rather than a math problem. (See “The Design of Everyday Things”, etc.) Still, it’s a fun one for discussion nonetheless! Thanks for sharing this!

This is an industrial design/ergonomics problem, with a bit of user interface design tossed in. The 0.9L flush button can’t be too small or it’ll be too difficult to press. All they really needed to do is represent one button as larger than the other, which they did. The curve is a nice aesthetic touch, but also serves the purpose of making the small button wider while still maintaining a smaller area. A straight line divison (see F) is too narrow, making it hard for fat fingers to push it. Along with the label, I’d say they pretty much nailed it.

On the economics of deciding whether to leave the seat up or down:
https://www.msu.edu/~choijay/etiquette.pdf
http://www.scq.ubc.ca/a-game-theoretic-approach-to-the-toilet-seat-problem/

On optimal design of toilet paper roll holders:
http://www.jnd.org/dn.mss/toilet_paper_algorit.html