Eureka!
No one seems to have noticed it, so I will draw your attention to the pattern at the bottom of the page which has replaced the panoramic view from my old office. If you scroll down to the bottom of the page, underneath the Earth Advisory Board notice, the WWW Deprication classification, and my home connection speed, you will notice a pattern consisting of white and blue squares.
Who can tell me:
1) What does this pattern represent?
2) Why is one square a darker blue than the others?
3) If you were to stumble upon this tile pattern on a wall, what would you expect to find behind the mis-colored blue tile?
Um... Memory barely there but....
ReplyDelete1. modular fibonacci sequence ( Fib(x) mod 5 )
2. It DOESN'T fit the pattern
3. I think there is a key to a safe deposit box behind it... I think... that or a tape player... I can't remember
ooh! ooh! I know! Cutting out the tile with George's handy-dandy pocketknife will reveal a key to a safety deposit box, which contains a tape recorder with a message informing you that the old geezer of blessed memory who was a math nut like yourself has just left you his entire fortune!
ReplyDeleteSigh, I miss Mathnet.
Hey, for my prize can I have a parrot that says "Five - Eureka!"?
Specifically, it's a key to a safety deposit box at the Next to Last National Bank. That's what I was looking for.
ReplyDeleteGood memory though. I had forgotten what was in the safety deposit box.
Of course I noticed it, but I was wondering why the extra square wasn't a link to anything.
ReplyDeleteIt is the fibonnaci sequence as Mr. Adams has noticed in base 5 with only the last digit displayed (i.e. 13 = 23 in base 5 so 3 is displayed) I don't see any special colored darker block, other than maybe related to astigmatism? If you crack the code, you get a free bag of marshmallows from google.
ReplyDeleteThis comment has been removed by the author.
ReplyDeletethe only thing I found odd about it was that the multiples of 5 should have resulted in 0 but instead in their diagram it results in 5. Didn't they explain why in Mathnet?
ReplyDeleteTrue. I didn't think of that... what about base 10 but subtract 5?
ReplyDeleteThe simplest answer to why the 0's show up as 5's is that the function is defined as some variation of mod 5. Not sure if there's a more complex explanation. Perhaps the columns with 0 colored squares would have been too confusing, so the producers decided to fill them in. If you simply count the squares (count up to 5 then start at the bottom for 6, count up to 10 then start at the bottom for 11, etc) then the coloring is correct.
ReplyDeleteI think it's easier to describe the Fibonacci sequence with the squares filled in; otherwise you have to describe Fibonacci and the modular function--one idea too many for a TV show. But I like the mod 5 interpretation; it's much tidier.
Never heard of Mathnet until I married into my current family. Sounds like a neat show.
Well, on the show, they essentially used the MOD function, only they talked about it as "the remainder". For 8, for example, I think they just counted up all 5 squares, then counted 3 more again from the bottom. Then they treated this new remainder as the seed for subsequent values. So the sequence on the tiles is actually 1,1,2,3,5,3,3,1 etc. The function for this is
ReplyDeletef(n) = ((f(n-1)+f(n-2)-1) MOD 5) + 1
for n > 1 and
f(0)=f(1)=1