Picture of Pythagorean Cup
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In this instructable I'm going to show you a simple way to make a Pythagorean cup. If you are looking for a cool peace of science, or would like to prank your friends, you came to the right place.

The special thing about this cup is that it can be used as a normal drinking cup as long as it is only filled with a certain amount of fluid. If a person is to greedy thought and fills it up to much, the entire content will empty through a hole in the bottom of the cup. It is named after the famous Ionian Greek philosopher Pythagoras of Samos (b. about 570 – d. about 495 BC), you might know him from the Pythagorean Theorem. I did a bit of research and found just as many sources saying that he did invent the cup, as ones saying that say he didn't.
So how does it work?
As you can see in the schematic on the left, there is a channel with an opening near the bottom of the glass running all the way through the stem to the base of it. As long as the fluid level stays under the inside loop of the cup, it can be used as normal. If too much liquid is filled into it though, a siphon is created and the whole glass empties.
Basically it works because the weight of the fluid flowing out reduces the pressure inside the tube so that the fluid is pushed into the channel by its own weight (Honestly this is not the entire truth, because a siphon also works in a vacuum, but enough to understand the effect. If you would like a more in-depth scientific explanation how siphons work, follow this link).

If you are interested in finding out more about the cup take a look at the wikipedia article and here are some great photos of someone making it out of clay. By the way this is the first thing I will make should I be able to afford a 3D printer, since I would love to see a version with the siphon hidden in the handle or the side of the cup.

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If this could be tested and proven to work in a vacuum, then my friend perpetual motion has been under our noses for quite some time! It is truly amazing what you can suddenly understand when presented with a tidbit of information!
Because it isn't so much "air pressure" as "surface tension adhesion" that makes it work, I do think it works in a vacuum. But it still isn't perpetual motion :-)
It'll work with water in a vacuum, due to the high surface tension. I suspect that with something with a low surface tension it won't work at all.

And of course you'll have troubles with the liquid trying to boil in the low air pressure.
Kaiven12 months ago

How does it behave when tilted? Can you drink out of it if there is a low enough level of liquid for added effect that the glass is normal?

BrittLiv (author)  Kaiven12 months ago
yes, you drink out of it.

Very interesting.

DUO00371 year ago
This would be so cool to prank my friends!
enelson81 year ago
I made one of these out of 123d so I wanted to know if you could check it out and see what needs improving. Thanks
BrittLiv (author)  enelson81 year ago
Hi, it looks great! The only thing I would change is to make the channel a bit bigger, so that the cup empties faster.
Btw. since I am to old to enter the 123d challenge feel free to do so. I will vote for you!
I don't know if I'm going to put this one on though because I already have one entered in. But do you think I should enter this in or do you think it would be wise to just say vote for my Ukuele instead?
BrittLiv (author)  enelson81 year ago
I would enter it and write a sentence like: "If you like this instructable, please also have a look at...". Enter as many as you can. More will increase your chances of winning (only won can end up winning of course), you will never know which one other people might prefer. I've won with stuff I wasn't a hundred percent convinced off and also didn't win with stuff I absolutely loved.
Ok thanks!
drinkstuff1 year ago
This is awesome! We were inspired to write our own blog article about the Pythagorean Cup and have included a link back to this page :)
youn_link1 year ago
I was sure that was the arquimides cup O.o but anyway gread idea to a party XD
Pythagorean_cup  whereas Archimedes spoke of mass and displacement., 
You MAY have been thinking of THIS CUP.
Goodhart1 year ago
Nice !
I have a much more complicated version of this in an OLD science project book. I am going to print this out and insert it near that page in the book, so I don't have to over think it :-)
aweith1 year ago
Omg that cup loove it. :P
Zwee1 year ago
I accidentally flagged this as inappropriate because I dropped my phone. Sorry!! Pls disregard the flag.
BrittLiv (author)  Zwee1 year ago
Hi, no need to worry, the admins will just delete the flag, should they not find anything wrong with it. I hope your phone is fine! Thank you for the subscription!
Edgar1 year ago
Gone to the blog:
BrittLiv (author)  Edgar1 year ago
Thank you! Interesting how I am able to read the Portuguese just by knowing Spanish.
Edgar BrittLiv1 year ago
My pleasure, well, it just shows you're clever, but some words mean different things, sometimes. Not often, though! :)
Just found out a video, completely off topic, but something to keep, when in dire need of a good laugh:
Edgar BrittLiv1 year ago
My pleasure, well, it just shows you're clever, but some words mean different things, sometimes. Not often, though! :)
Just found out a video, completely off topic, but something to keep, when in dire need of a good laugh:
bajablue1 year ago
So clever, Britt... and the Vote button is, too!!! Can the less-computer-saavy of us look forward to an Instructable on that?
BrittLiv (author)  bajablue1 year ago
(removed by author or community request)

On an Html Saavy Scale of 1-10, I'm a ½, but I think I can do this! (she said with her fingers crossed ;-)  I'll need to print these instructions when I'm connected to a printer back home.  I'm excited to try it!

Thanks so much for 'splainin!!!

One more question: Can you put the "Vote" link anywhere on the web?

Thanks for your time!!!

BrittLiv (author)  bajablue1 year ago
No problem, sadly it won't work since whoever would want to vote has to be logged in to instructables.
Actually, that's a very good thing! ;-) Thanks again!
BrittLiv (author)  bajablue1 year ago
Hi, I'm really sorry, but it doesn't seem to work any more, once you hit publish some of the code vanishes, so that the button becomes useless. Looks like the admins didn't like the idea of putting a vote button inside of an ible.
Well drat. Looks like the great and powerful oz has spoken. O_o
Jakwiebus1 year ago
I was puzzling how to make this for some time. Kept me awake... Apparently I was over thinking this big time :D
you kept it simple but good,
love it!
+1 vote
BrittLiv (author)  Jakwiebus1 year ago
Thank you! Yes, it is a very simple concept. You don't even have to glue the tube to the glass, I just didn't want it to fall out.
babybayrs1 year ago
Just clicked the vote button at the end (is it a prank?) It seems I have to prank my greedy friends always in their place if I don't want the fluid to empty to my table, right?
BrittLiv (author)  babybayrs1 year ago
Hi, thank you for voting! The button is not a prank I figured it be easier to have it in the text instead of just having it on the top of the page, where it is harder to spot. Have fun pranking you friends! Yes, the cup is better used outside, or at a friends place ;-)
Thanks for confirming. You are so talented. I loved your idea of the cup and putting the button at the end.
jimmytvf1 year ago
if you put a lid on the bottom, if you overfill the glass for accident, you won't spill anything. it could be pretty useful
Edgar1 year ago
Nice work, BrittLiv, and talking about Ancient Greeks, I'm wondering if you saw this:
There's a Wiki, too, and guess what, you can make a Archimedes Puzzle:
BrittLiv (author)  Edgar1 year ago
I didn't know the video, thank you for showing it to me! It is very interesting.
Very cool. It looks well constructed
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