Toned paper is indeed great to work with! I use sepia colored fin liners, a set of varing shade brown markers, and a white gel pen =) ]]>

When I saw the year you have posted I was hopeless to receive an answer. It clarified the figure at all. Thank you to spent a time recovering the material to give me the answer.

Cheers,

João

]]>Glad you had fun reading! (Haven’t been looking at train tracks for a long time! You made me look at them again, was fun!)

So, the last diagram isn’t meant to actually having the number of curves added up; as we were sating, the weight can be any positive real number, not only rational numbers; what I meant here is that, given any triple of positive real numbers (e.g. 1, 1/2, 2/3) there is a way to assign weights to the branches where they match all 3 on the cuffs. In this example, the thin branch on the right would carry a weight of 1/12, so that we have (1/2-1/12)+(2/3-1/12)=1. Agree that to be actually accurate I should have put 12 lines in the left cuff, 6 in top and 8 in the right.

Hope that helps~

Cheers,

C

Your blog is amazing and the drawings are realy well done. However I’m having some trouble to understand the last figure in this post. Specifically the numbers 1, 2/3 and 1/2. No matter how I count the branches of the train track the weights doest fit it.

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