I occasionally find myself with a lump of dough which I want to divide into three equally sized pieces (like for making 3 pizza bases). I could weigh it but it typically means getting the scales out and dirty and having to cut pieces off and re-knead them into the dough. Eye-balling kinda works but sometimes I'm a fair bit off.
So I was wondering if there is a nice technique which doesn't require additional tools like a scale to divide a lump of dough into three equally sized pieces?
You could measure it out using your hand. Roll out the dough to be close to the width of three hands, and then cut each piece at the width of your hand. It is fairly easy to make an even roll, and the width of your hand is fairly constant, so that should make for three closely sized lumps of dough.
Added: Another variant using a measuring trick, is to first make an even roll, then use the tip of your digits(/fingers) not including the thumb to make a line of dots along the length of the roll. Then you can count the dots and divide by three.
Another trick: make an evenly roll, lay it down in a S-form and push it together. It works quite well after a bit of practice. Main advantage: you can add more "loops" to make 4, 5, and more parts. The roll needs to be thinner and thinner, so there is some natural limit to it but even I with my all-thumbs hands can manage up to 7.
Why not using the simple fact that cos(60°) = 1/2?
Put your dough in the form of a circle, make sure you know the centre point. From there you draw a horizontal line to the right, and in the middle of that line, you draw a perpendicular line up and down. Like this, you find two points, one above and one beneath. Together with the outmost left point of your circle, this forms the edges of the third parts you are looking for.
Here's an old math trick that makes dividing dough into thirds easy.
Try fashioning an equilateral (all 3 sides of the same lenght) triangle with the dough. Make sure it is level (height needs to be uniform). Then, simply cut the dough in half from each angle of the triangle (so 3 cuts). You'll get 6 pieces of equal mass. Add these pieces 2 by two and you get 3 pieces of equal mass.
[EDIT, since it was requested in the comments, here's a little addendum : if you don't want 6 pieces, simply don't make cuts all the way through in length. Stop cutting at 2/3 of the length between the corner and the opposing side of the triangle (see picture). You really don't need to be accurate there.]
The solution doesn't remove the need to be accurate, but makes being accurate easier (the geometrical form will favor accuracy, as it is more visual than simply guessing the size of each piece).
Choose any other geometrical form if you need to make more pieces (a square for 4 pieces, etc...)
Start with a square. Divide it into four sub-squares. Set aside three of the sub-squares. Divide the remaining sub-square into four sub-sub-squares. Add one sub-sub-square to each of the three intact sub-squares. Divide the remaining sub-sub-square into four sub^N-squares. Continue the process until one of the remaining sub^N-squares is so small that you don't care if it isn't perfectly divided into thirds.
Assuming that you can split the dough in half accurately:
Divide to three pieces arbitrarily, then just cut away and eat slices from the currently biggest part until all three pieces are equal.
Break off a piece such that the remaining piece is twice as large. Then break that large piece in half.
