Replies

1. 
   MrBill | Jun 29, 2009 03:13am | #1

   Pell,

    It is because of the way the 6/12 and 12/12 is measured. Angles are based on a circle which is 360 degrees. If you draw it on paper you will see what I mean. If you start at a point, a line drawn at 6/12 pitch will be more than half of that drawn at a 12/12 pitch. Kind of hard to describe without drawing it. Maybe I will see if I can make a drawing and scan it in ?

   Bill Koustenis

   Advanced Automotive Machine

   Waldorf Md

2. 
   mike_maines | Jun 29, 2009 03:17am | #2

   Picture a circle with a 12" radius.  A line drawn from the center horizontally to one edge, 12" long, represents 0°.  Vertically, the line represents 90°.  Halfway between is 45°.

   Now picture a 12" x 12" square.  The base of the square is 0°.  Draw a line from a bottom corner, halfway up the other side.  That line is a 6/12 pitch.  Draw a line from the bottom corner to the diagonally opposite corner.  That line is a 12/12 pitch. 

   Note that in the circle, the line stays the same length.  In the square, the length of the line changes. 

   If the line within the square did not change length, but rotated from 0° to a line cutting across the center of the square, it WOULD be 45°.  Instead, because its length increases, the angle is effectively reduced.

    

3. 
   DanH | Jun 29, 2009 03:21am | #3

   The short answer is because circles ain't square.

   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz
1. 
   FastEddie | Jun 29, 2009 03:31am | #4

   Pi are square."Put your creed in your deed."   Emerson

   "When asked if you can do something, tell'em "Why certainly I can", then get busy and find a way to do it."  T. Roosevelt

1. 
   rich1 | Jun 30, 2009 07:42am | #29

   Pie's are round in my world.

2. 
   JTC1 | Jul 01, 2009 03:29am | #34

   >>Pi are square.<<

   No, NO, No, No,........

   How many times does this have to be splained ----

   pi are round

   .

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    cake are square!

   JimNever underestimate the value of a sharp pencil or good light.

1. 
   rich1 | Jul 01, 2009 07:44am | #40

   Sooooooooooooo.....................why are manhole covers round?

1. 
   DanH | Jul 01, 2009 02:26pm | #42

   Because the manholes are round, silly.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

2. 
   Jeff_Clarke | Jul 01, 2009 03:00pm | #44

   Sooooooooooooo.....................why are manhole covers round?

   Because round covers can't fall through the hole and rectilinear ones can.

   Jeff

3. 
   DanH | Jul 01, 2009 09:03pm | #45

   Depends on the shape of the hole, doesn't it?
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

4. 
   jonblakemore | Jul 01, 2009 09:06pm | #46

   Can you make a rectilinear shape that cannot fall through it's own "hole"?The only way I can see that being true is if you have a lid that is thicker than the shape in the short dimension. 

   Jon Blakemore RappahannockINC.com Fredericksburg, VA

5. 
   DanH | Jul 01, 2009 11:23pm | #47

   Just gotta make the lid sufficiently larger than the hole.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

6. 
   jonblakemore | Jul 02, 2009 12:09am | #48

   Oh, I assumed you were being practical. 

   Jon Blakemore RappahannockINC.com Fredericksburg, VA

7. 
   DanH | Jul 02, 2009 12:51am | #49

   Make the lid smaller than the hole and even a round cover will fall through.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

8. 
   Jeff_Clarke | Jul 02, 2009 03:45am | #50

   A lid smaller than the hole isn't a lid.

9. 
   DanH | Jul 02, 2009 03:52am | #51

   Depends on what the lid is comprised of.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

3. 
   maverick | Jul 01, 2009 05:44am | #38

    2 Pi r squared

   1 pie are food

1. 
   DanH | Jul 01, 2009 06:06am | #39

   2 Pi are area
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

1. 
   maverick | Jul 01, 2009 02:51pm | #43

   squared

4. 
   Huck | Jun 29, 2009 03:35am | #5

   hopefully, this diagram will show that even 'tho numerically 6 is half of 12, a 6:12 roof pitch is not truly half of a 12:12 roof pitch

   View Image

   View Image

   
   

   ---

   Edited 6/28/2009 8:45 pm by Huck

1. 
   Boats234 | Jun 29, 2009 04:43am | #8

   Pictures are worth a thousand words.....perfect.

2. 
   brucet9 | Jul 01, 2009 02:55am | #32

   Thanks for the clear explanation of 6-12 12-12.Now can you explain why in your diagram what must have been a section of a circle shows up here as a section of an ellipse?BruceT

1. 
   DanH | Jul 01, 2009 02:59am | #33

   Curvature of the earth. As you get closer to the poles one dimension is compressed vs the other.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

1. 
   brucet9 | Jul 01, 2009 03:35am | #35

   So that's why it's so hard to measure the roof pitch of igloos?BruceT

5. 
   BossHog | Jun 29, 2009 03:50am | #6

   I aswered the same question back in 2002, and I miraculously found the thread. Here's my answer from back then:

   Start out with a 1/12 angle, which is 4.8°. This triangle is 12" across the base, and 1" on the vertical leg.

   Take a 2/12 angle, which is 9.5°. This triangle is 12" across the base, and 2" on the vertical leg. Subtract the 1/12 angle of 4.8° and you'll notice that this angle has only increased by 4.7°.

   Then look at a 3/12 angle, or 14.0°. That is only an increase of 4.5° from the 2/12 angle. (The "law of diminishing returns", I guess.)

   Take the diference between a 12/12 angle (45°) and 11/12 (42.5°) and you'll see the difference is only 2.5°.

   When you take a 45° angle and divide it in half, you're dividing an arc in half. When you deal with roof pitches, you're dealing with right triangles with different lengths on the vertical leg. (The horizontal leg is always 12")

   -------------

   This question comes up with regards to trusses every once in a while. There's a rule of thumb that architects like to use that "any scissor truss will work, as long as you have a 2/12 difference between the top chord and bottom chord". But that's not always true.

   Take a scissor truss that's 4/12 (18.4°) on the top chord, and 2/12 (9.5°)on the bottom chord. The relative angle between the top and bottom chords is 8.9°.

   But change the pitches to 8/12 (33.7°) over 6/12 (26.6°) and the relative angle is only 7.1°. The truss may not work, or may have too much horizontal deflection.

   That oughta either answer your question or bore you to tears.

   Bumpersticker: Can't feed 'em - Don't breed 'em

6. 
   mike585 | Jun 29, 2009 04:06am | #7

   It's because circles are curved an lines are straight. The mathematical function for a circle is X **2 + Y** 2=r**2 (the **2 means squared). The squaring makes it not linear when figuring the angles.

7. 
   9ENGEL | Jun 29, 2009 06:46am | #9

   Because slope goes to infiniti.

   Ask your crew,"If a horizontal line is a 0/12, and a 45 deg line is a 12/12, what is a vertical line?".

   So there is no whole to be half of.

1. 
   mike585 | Jun 29, 2009 08:20pm | #10

   a vertical line would be 12/0

1. 
   DanH | Jun 29, 2009 09:22pm | #11

   infinity/12
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

1. 
   Huck | Jun 29, 2009 09:47pm | #12

   infinity/0View Image

1. 
   DanH | Jun 29, 2009 11:09pm | #13

   No, infinity over 12. You've got 4/12 pitch, 6/12 pitch, 12/12 pitch. Vertical is infinity/12. (Or infinity divided by any other positive number.)
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

2. 
   BossHog | Jun 29, 2009 11:14pm | #14

   To me, vertical is just vertical. It can't be anything over zero, as you can't divide by zero.
   Bumpersticker: Get revenge - #### on a pigeon

3. 
   Huck | Jun 29, 2009 11:52pm | #16

   roof ratios are rise/run.  a 6/12 roof pitch rises 6 units for every 12 units of run.  A 12/12 roof pitch rises 12 units for every 12 units of run.  Etc.

   If a vertical line rises indefinitely with no "run", then it is infinity/0.  But, of course, it could be any positive number/0.  While theoretically infinity/12 would have the same eventual outcome, it is faulty as a roof pitch ratio, because there would be no run on a vertical line.  Which is all kinda silly, because there could be no such thing as a vertical roof rafter! You'd have to build a pitched roof on top of it!

    View Image

4. 
   BossHog | Jun 30, 2009 12:03am | #17

   Sounds to me like this could go the same way as some of the other math arguements here on BT.This time I ain't goin' along for the ride.
   Two things are infinite: the universe and human stupidity; and I'm not sure about the universe. [Albert Einstein]

5. 
   mike_maines | Jun 30, 2009 12:08am | #19

   So there's an airplane on a treadmill....

6. 
   BossHog | Jun 30, 2009 12:56am | #22

   But what pitch is the treadmill at? And what percentage is the rise??
   I may not be totally perfect, but parts of me are excellent. [Ashleigh Brilliant]

7. 
   mike_maines | Jun 30, 2009 01:14am | #23

   LOL

8. 
   mike585 | Jun 30, 2009 01:30am | #24

   You have to alter your mind in some way and then think on it. You then reach a higher state of roof framing consciousness that no one understands or is willing to pay for.6/12 is for unenlightened people.

9. 
   Huck | Jun 30, 2009 01:41am | #25

   You have to alter your mind

   uh, no thanks

   a higher state of roof framing consciousness that no one understands or is willing to pay for.

   you mean like Marshal Gross?View Image

10. 
    fingersandtoes | Jun 30, 2009 03:45am | #26

    "you mean like Marshal Gross?"

    Gerry Garcia?

11. 
    mike585 | Jun 30, 2009 04:47am | #27

    A good read. Still have my copy.

12. 
    KaneoheBay | Jul 01, 2009 12:57am | #31

    Mathematically, anything divided by zero is "undefined."

13. 
    cussnu2 | Jun 30, 2009 12:03am | #18

    But if it is a verticle line, then it has no pitch thus only rise no run. Thus, I agree it would be infinity over / 0 if you were trying to express it in a similar fashion to a 12/12 pitch.  Look at it this way, you have a 12"/12" pitch  getting closer to verticle you would have a 12" / 1" pitch then say a 12" / 1/32" pitch  thus the closer you get to verticle the closer you necessarily get to 0  the slash in this instance is not a symbol of division thus there is no dividing by 0.

14. 
    DanH | Jun 30, 2009 12:41am | #20

    But roof pitch is generally expressed in x/12 notation, and the OP's understanding of the confusion is best facilitated by maintaining that notation up through 12/12, 18/12, 24/12, etc. Taken to the limit it's infinity/12.
    As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

15. 
    JMadson | Jul 01, 2009 03:56am | #36

    But roof pitch is generally expressed in x/12 notation

    This is just like the discussion in baseball about how many games over five hundred a team is. People are trying to mix real math with fabricated math terms that only make sense when you know the relavant deifinition. 

     

16. 
    Jeff_Clarke | Jul 01, 2009 04:29am | #37

    I think I *finally* understand ;o)So please explain if 12/12 is 45 degrees and a vertical line is infinity/12 why 12 isn't half of infinity???Jeff ;o) 

2. 
   mike585 | Jun 29, 2009 11:31pm | #15

   But I can't find infinity on my square, so I use 0/12 and flip it over.

2. 
   woodway | Jun 30, 2009 07:31am | #28

   And, infinity can't be reached!

1. 
   DanH | Jun 30, 2009 02:26pm | #30

   Yeah, but an Infiniti can be pinched.
   As I stood before the gates I realized that I never want to be as certain about anything as were the people who built this place. --Rabbi Sheila Peltz, on her visit to Auschwitz

8. 
   doodabug | Jun 30, 2009 12:52am | #21

   It kinda is. a 12/12 is 1/2 pitch and a 6/12 is 1/4 pitch. Old talk.

   Just not 1/2 the degrees. I call 5/12, 22 1/2 degrees but it is 22.63 actually.

   If you draw those lines in a 1' square box it is easier to visualize.

9. 
   BobRat | Jul 01, 2009 09:00am | #41

   If you want the quick answer without trying to understand - you can use google

   for 6/12 type into google -- arctan (6/12) * (180/3.14159)

   for 12/12 arctan (12/12) * (180/3.14159)