Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to achieve something similar to Bret Victor's brilliant Scrubbing Calculator in Mathematica.

By using Manipulate I'd like to change the values of the variables such that if I modify one the others adapt to ensure the equation is always true.

In the example below I'd like to be able to move spaces and have boxes change accordingly.

Manipulate[4 spaces + 3 boxes = 640, {spaces, 0, 640}, {boxes, 0, 640}]

The simplest case

Solving for the two variables explicitly I can achieve the desired effect but doing so kind of voids the idea of an intuitive calculator.

Manipulate[{Dynamic[spaces = 160 - (3 boxes)/4], 
  Dynamic[boxes = -(4/3) (spaces - 160)]}, {boxes, 0, 640}, {spaces, 
  0, 640}]

The hard way

Now, kind Mathematicans, my question is this:

Is there a way of doing this the first, more intuitive, way?

share|improve this question
Could you please post copiable code so that whoever wants to give solutions can easily do that? – István Zachar Apr 13 '12 at 15:55
Ok, you've added it. thanks. – Teo Sartori Apr 13 '12 at 16:25

Well, I have needed before to link variables within a manipulate object, and I always get complicated dynamic things, for your example if you want to add constraints to your variables, you could come up with something like this:

Module[{spaces, boxes, lastboxes, lastspaces, condition, solvebox, 
 condition[s_, b_] := 4 s + 3 b == 640;
 solvebox[s_] := b /. First[Solve[condition[s, b], b]];
 solvespace[b_] := s /. First[Solve[condition[s, b], s]];
 lastboxes = 100;
 lastspaces = solvespace[lastboxes];
 Manipulate[{spaces, boxes}, 
  Control[{{boxes, lastboxes, "Boxes"}, 0, 640}], 
  Control[{{spaces, lastspaces, "Spaces"}, 0, 640}], 
  Dynamic[If[! condition[spaces, boxes], 
    If[lastboxes === boxes, 
      With[{newbox = solvebox[spaces]}, 
       If[newbox < 0, spaces = solvespace[boxes], lastboxes = boxes; 
        boxes = solvebox[spaces]]], 
      With[{newspaces = solvespace[boxes]}, 
       If[newspaces < 0, boxes = lastboxes, lastboxes = boxes; 
        spaces = newspaces]]];]; ""], ControlPlacement -> Left, 
  Deployed -> True]

That Dynamic after Control objects comes pretty good to do that stuff, but does your code become bigger.

share|improve this answer
Thank you for your answer. This does indeed achieve the same result, but doesn't quite manage to do so in a simpler, more intuitive way. It is quite possible that what I'm asking is not possible in Mathematica. – Teo Sartori Apr 14 '12 at 8:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.