Road Sign Math

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April 5th, 2006 · 10 Comments

Pennsylvania

David Slauenwhite brings us a huge sign from Pennsylvania! This sign that is barely visible behind all the numbers presents a slew of opportunities. The scenic lumberyard in the background is Ron Baltzley Hardwoods, a member of the Northern Tier Hardwood Association.

Mr. Slauenwhite nails Euler to 4 decimal places on this sign! However, he takes a dreaded 50% deduction in his score for this sign for using cancelation math (note the 660 - 660). Due to a judging error this sign was originally penalized for cancelation math, however, it was later determined to be incorrect.

{{4\times(2005-660-660)\times\tan{45^\circ}} \over {(2005+380-370+1)\times\sin{390^\circ}}} \rightarrow {{2740}\over{1008}} \approx 2.718253 \approx e

This sign is in Covington Township, Pennsylvania at the junction of SR660 and SR2005. See sign on map!

Tags: Pennsylvania

10 responses so far ↓

  • 1 Geof F. Morris // Apr 6, 2006 at 3:30 pm

    How is 2005-660-660 cancellation math? I understand it if it’s 2005+660-660.

    GFM

  • 2 Road Sign Math Administrator // Apr 6, 2006 at 8:17 pm

    The 660 - 660 yields 0, it doesn’t matter if that zero is then being added or subtracted, the effect is that the two 660’s have effectively been cancelled from the sign.

  • 3 Geof F. Morris // Apr 6, 2006 at 10:10 pm

    Well, again, I would understand that if it was stated as (2005-(660-660)), but 2005-660-660 is 685, not 2005. Indeed, 4 x (2005 - 660 - 660) = 2740; 4 x (2005 - (660 - 660) ) = 8020.

    I’m aware that it looks like cancellation mathematics, but it’s not.

  • 4 Todd Southworth // Apr 7, 2006 at 2:31 am

    I would agree that 2005 - 660 - 660 is not a cancellation and should not be penalized. The first operation is to subtract 660 from 2005 (yielding 1345), the second is to subtract 660 from the result (yielding 685). I do have a question about multiplying by tan 45°, however. Since tan 45° = 1, is there a penalty for multiplying by one?

  • 5 Road Sign Math Administrator // Apr 7, 2006 at 6:39 am

    Ok, in my zeal to get caught up on my backlog of signs I was too quick with this sign, clearly. Form over function. Geof and Todd are correct, this is not a violation of cancelation because you do not leave the parenthised (?) section with the same number you start with.

    To amplify on Todd’s question regarding the tan 45°. While this does yield 1, cancellation rules only apply to the first form of the equation, and not any intermediate steps. This is more clear with the example of x/x. This cancelation yields one, but only causes a penalty for the x/x, without any additional penalty for x * 1.

  • 6 Road Sign Math Administrator // Apr 7, 2006 at 6:39 am

    PS - It’s great to know that the readers of RSM are not only just reading, but calculating as well! :-)

  • 7 David Slauenwhite // Apr 7, 2006 at 8:31 pm

    Thank you to everyone who helped in "canceling" the penalty before I even had a chance to click back to look at this page.

  • 8 jim bernard (jr) // Apr 7, 2006 at 8:41 pm

    They may be unaware that you have a bounty of points and didn’t need the help! ; >

  • 9 Geof F. Morris // Apr 7, 2006 at 9:09 pm

    Hey, I just want the right stuff to be put out there. I can understand where the mistake was made, especially if you get lots of submissions and don’t have time to review them all. It’s not like we’re paying your bills. ;)

  • 10 jim bernard (jr) // Apr 7, 2006 at 9:19 pm

    Well it is a math site. I think we’ll all sleep better knowing that the score is correct. Even if it just adds to David’s massive total.

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