Tuesday Inlay

Re: Tuesday Inlay

Alex Y

Thanks for this "woodifying" of a classic! But memory failed me and I had to resort to Google, so I will sit this one out.

If I remember correctly the USGS confronts

Gary Smyth

the same problem. Same dilemma different medium.

More inlays and more coffee

Bill Earl

Looks like Alex and Gary know the answer. But can they prove it?

A customer requests a custom wooden globe. How many kinds of veneer does he need for that?

This woodworker's cousin is a ceramist and creates similarly intricate patterns on all exposed surfaces of of his wares. How many colors of glaze does he need for a bowl? How many for a coffee cup?

Proof! proof?  I don't need no stinkin

Gary Smyth

proof. I'm no engineer or math person. Alex may have a engineering proof. I tend to remember what I read. When I was in school, the number was six. That was reduced to five when white was not allowed as a color. Before I was out of school, with the computer testing actual maps that was reduced to four. As far as I know, there is no actual math based formula, only that there are no examples anyone has discovered that dispute four is the lowest number required for a flat surface. This is a map makers question that has been around for a long time and older maps will use five colors (and black). If the shape is different than two dimensions then other factors have to be entered. For a flat inlay surface other additional colors need not be considered. The answer was by a guy named Apple and it took a computer (not the same thing) scanning every map they could find and number crunching to get the existing lowest number.

Bill Earl

The 4-color theorem is more of a mathematical problem than a cartographical one. (Real cartographers just buy more ink.) It went unproved for many years - and the proof was disputed for several years more. The bulk of the work (testing all possible exceptions) was done by computer, but there were thousands of pages of test cases and results that had to be checked by hand.

The 5 color theorem is a moderately difficult one (that I have mostly forgotten ) discovered in the process of attempting to prove the 4 color theorem. But it was almost another 100 years before there was a proof for 4-colors.

Re: More inlays and more coffee

Alex Y

I would ask that guy who pours coffee on donuts.

I would suspect the answer is 4 for the globe and bowl, and would not be surprised if it were higher for the cup.

But those are just guesses.

Bill Earl

And good guesses they are. Our topologist friend from last week can't tell the difference between a bowl and a sphere. Like a 2 dimensional surface, both of those can be colored with no more than 4 colors.

The coffee cup is a torus and somewhat more complicated. It can take as many as 7 colors for a torus.

There is one lesson I have not forgotten from my long-ago studies: The proof is always left as an exercise for the reader.