Pythagorean Cup





Introduction: Pythagorean Cup

About: Hi, my name is Britt Michelsen, I'm a Chemical Engineer especially interested in Computational Fluid Dynamics. To balance all the theoretical work I like to make stuff in my free time.

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.

Step 1: What You Need

What you need

  • Plastic wine glass (best are non transparent ones)
  • Silicone glue
  • Straw (best is a transparent one)
  • Plastic test tube (slightly bigger than the straw)
  • Box cutter
  • Small saw

Step 2: Sawing

I used a transparent cup for you to better see what I am doing, but I suggest you use a non-transparent one.

Start by sawing off the bottom of the top part of the cup, as shown in the first picture. Make sure, that the straw fits through the hole. Afterwards use the box cutter to carefully drill a hole into the bottom, as shown in the third picture. The straw will have to fit through this hole as well.

Step 3: Glue Everything Together

The length of the straw defines the amount of fluid the cup can hold. Since it is difficult to cut it once it is glued in place, you should do it beforehand.

Fill the stem of the cup with silicone adhesive around the straw, to hold it in place and to prevent the liquid from flowing into it. As shown in the first two pictures above.

Afterwards you will have to cut the tube to the correct length. It has to be bit longer than the straw. Cut a small hole into the bottom, to allow the liquid to flow into it, as shown in the pictures. Then apply the silicone adhesive around the rim and place it above the straw. Let everything set and you are done.

Make sure not to use the cup above a valuable carpet or something similar. If you don't want the inside to be visible, just fill the cup with ice.

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    48 Discussions

    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!

    3 replies

    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.

    We could test that with something like diet soda, which has a low surface tension.

    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?

    1 reply

    yes, you drink out of it.

    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

    4 replies

    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?

    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.

    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 :)

    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 :-)


    5 years ago

    Omg that cup loove it. :P


    5 years ago

    I accidentally flagged this as inappropriate because I dropped my phone. Sorry!! Pls disregard the flag.