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Pythagorean cup (wikipedia.org)
109 points by heeton on June 1, 2014 | hide | past | favorite | 41 comments

Beautiful. This has a modern application. When fed with a slow trickle of water, it will empty itself periodically, and formed the basis of automatic-flush urinals before the electronic valves became commonplace.

Doesn't a flush require that water be added fast enough to eliminate all the air from the bend? Otherwise, water will just trickle out at the same rate it trickles in.

Yes, it has to do that. The bend may have to be narrow enough for surface tension to have an effect.

I found this nice web page, the Virtual Lavatory:


Interesting, but goofy in spots:

Why did Britain evolve such a complex mechanism when this pattern seems so simple? Water economy: these valves can leak and can be kept permanently open, allowing precious gallons to be wasted.

I've never been to Britain, but my impression is that it's not a particularly dry place. Why would "water economy" be so much more important there than in e.g. Israel or California? Perhaps toilet technology is as path-dependent as any other evolutionary process?

Just curious: I understand why titles might be reset to the raw title found on the page, but in this case it's just made the headline less useful.

I added a tiny bit of context when posting - to explain to people why this might be interesting to them. "Pythagorean 'greedy' cup - empties entirely if filled too much".

What's the purpose of reducing that to just the raw wikipedia title?

Your added context worked for me. I saw your original title but did not have time to read an article, but your title interested me enough that I noted to myself to come back and read it later.

I would have skipped it under the current title.

Thanks, I thought as much. I certainly noticed that it got a lot of votes - title changed - and it started to get much fewer upvotes, indicating that less people bothered to read it.

I was the same. I saw the full title in the morning and thought it looked interesting enought to read later. When I came back the title had changed and I wouldn't have clicked through had I not seen the explanation in the original title.

Glad I did, too, because it's such a clever "gadget"!

Hypothesis: It's more 'smartass' without the context. More obscure, etc.

My first thought was, wow, they could have had computers based on sets of these connected in different ways, as logic circuits. As I recall from the Stephenson version, Turing and co. were using something similar in the analog days.

Yup it's definitely possible http://en.wikipedia.org/wiki/Fluidics

Clever, but isn't there some danger that if you tipped it the wrong way when drinking out of it, even before the "gluttony" level, that you'd start up the siphon action, causing it to empty out onto the floor? At the very least you can imagine you'd get a bit of wine trapped in the curve, which would then drip out of the hole at the bottom.

I don't think so, because the column is in the middle; as long as the tube in the middle is narrow, whichever way you tilt it the height in the centre will be the same as it was at the start and nothing comes out. I guess if you tilt it past horizontal to drink out of while the cup's more than half full then you have a problem - but that sounds more like a feature than a bug.

Yes, upon seeing this I immediately wanted a 'trick' cup that did this but had this, umm, feature more hidden by placing it in the side of the cup not the middle. But then an unsuspecting, but non-greedy, user may spill the entire cup just by sipping out of the wrong side! The central column should make it quite safe in comparison.

Even I got the same Question in Mind.

Answer to this question can be found by only two ways (I feel So) either by using the cup or asking someone who has used it.

Can we get this kind of cup any where online?

There are several 3D models available online that could be trivially 3D printed.

Wouldn't it be easier to simply have a smaller cup? I mean, this is clever, but seems a tad impractical.

The point is to punish gluttony, but even that point isn't the point. The point is to demonstrate a system with a threshold. a tank fills to a point, and rather than overflowing the tank, completely empties it.

A more obvious subversion of this would be to stick your finger in the discharge at the bottom. Fill it as much as you want then.

Here is a 3d printable version :) Work in progress...enjoy.



BTW, shapedo has a tool to migrate all your thingiverse items over with one click :)

A good video explaining it:


That is a copy. Here is the original video from the original channel: https://www.youtube.com/watch?v=kb5N2wpYRJg

I love this idea! I wonder if someone could make a 3D model that could be easily printed of one.

This principle is used in aquaponics in the form of a bell siphon. You don't want to keep the roots of your plans submerged for long periods of time, so this lets you flush out the water automatically.

As noted on the article talk page, it's rather dubiously sourced that this device really goes back to Pythagoras. The tourist wares shown in the article photographs are of course much newer than that.

It seems unlikely that this would have been used as a drinking cup, because it wouldn't work properly if it's moved around or tipped. Instead, it was probably a "temple magic" device, where a worshipper would have to buy some sacrificial wine and pour it into a mounted cup as a sacrifice. If they don't pour enough in, nothing happens, but once they pour enough the god "drinks" the wine. The wine probably fell down into a bucket attached to some mechanism that would make noise, or move something, or maybe open a door, to indicate that the god is satisfied with the sacrifice.

The water level in the center does not rise when you tip a cup. Sloshing back and forth does the same thing the only edge case banging the cup on a surface but given a small internal channel that's not going to do much either.

PS: My initial thought was incaseing the channel in the edge would be less obvious but that would have more issues with tipping.

If the siphon is in the middle of the cup, it won't be activated by tipping, because tipping won't increase the level at the centre.

It could definitely be used as a drinking cup, and would work the same even when occasionally tipped.

The only moment it can spill is when you fill it, at which point it would likely be in horizontal position.

That sounds highly speculative.

This cup seems like one of the trick cup that you give to your friends after they had a few pints of beer.

Those Greeks, funny guys!

Wouldn't it be easier to have the hole go straight up through the center shaft without looping around?

Then it would only remove the excess, not the entire contents.

The linked design only removes the excess too.

It seemed to me that the linked design removed the entire contents: "Hydrostatic pressure then creates a siphon through the central column, causing the entire contents of the cup to be emptied through the hole at the bottom of the stem."

Is this how a regular toilet works too?

Yes, it's also based on communicating vessels and syphon effect.

I implemented this design in LiquidSketch game on iPad some time ago. Amazingly it worked.

Cool concept, though not very practical (just like so many other ideas). Sounds like the Spork of it's time :).


Because it's not as funny, and because this functions as an alert to tell everyone when you lose awareness of how far you're filling it.

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