Subject: Pyramid (Compound angles)

From: [email-masked] (Randy Reid)
Date: 28 Mar 1997 20:58:32 GMT

Can anybody out there give me the formula for figuring out the angles to
construct a four sided pyramid?  I know there is one but for the life of
me I can't find it.  Thanks for any help you may be.
 e-mail to :    [email-masked]

-- 
[email-masked]

---

From: [email-masked] (Tom Gauldin)
Date: Fri, 28 Mar 1997 22:06:19 GMT

Download the files about hoppers from my ftp site.

ftp://ftp.mindspring.com/pub/users/scoundrl  One file is an excel-type
spreadsheet that calculates the settings based on the number of sides, while
another is based upon the angular differences.  The third file is a printout
of settings for the most common of 3,4,5 6-sided figures with angles ranging
>from  2 degrees upward by 2 degree increments, including 33-1/3 and 45 degrees.

There are some other woodworking files in the site      ftp_anno.txt is the
index file.

Tom

Tom Gauldin           Here's to the land of the longleaf pine,
Raleigh NC             The Summerland,where the sun doth shine.
fax 919-676-1404   Where the weak grow strong,and the strong grow great,
                               Here's to Downhome,the Old North State.

---

From: Bill Pounds <[email-masked]>
Date: Fri, 28 Mar 1997 20:41:14 -0800

>  e-mail to :    [email-masked]

There is a very nice shareware program for MS Windows which is exactly
what you need. It's called miter and you can find it at the Wood
Magazine site. To download it, go to;

http://www.woodmagazine.com

-- 
Bill Pounds
[email-masked]
http://www.netcom.com/~bpounds/index.htm
**********************************************
* Join the National Rifle Association today. *
*  The rights you save will be your own!     *
**********************************************

---

From: [email-masked] (Pete Wilson)
Date: Sat, 29 Mar 1997 15:03:01 GMT

In article <[email-masked]>,
> e-mail to :    [email-masked]

Could you please post to the group as well? Very useful for other 
stuff that _resembles_ triangle. Didn't know such a formula existed.

---

From: [email-masked] (Pete Wilson)
Date: Sat, 29 Mar 1997 15:21:11 GMT

In article <[email-masked]>,
Bill Pounds  <[email-masked]> wrote:
>> construct a four sided pyramid?
<snip>
>http://www.woodmagazine.com

Real nice site. Real nice-looking PC (no Mac) software: 

--Inch-Foot-Fraction Calculator: Add, subtract, multiply, and divide 
    measurements in feet, inches, and fractions of an inch. 
--Miter Calculator: Calculates miter and compound-miter angles for 
    figures of up to 50 sides.
--Dovetail Template Maker: Produces templates for dovetail joints. 
--Sheet Layout: Generates cutting diagrams. 
--Tool Journal: A database to keep track of your tools and equipment.
--Shop Designer: Lay out a floorplan for your shop with this program.
--Molding Calculator: Determines miter and bevel angles for crown moldings. 

>Bill Pounds >[email-masked] >http://www.netcom.com/~bpounds/index.htm
x-no-archive:yes

---

From: [email-masked] (Tom Gauldin)
Date: Sat, 29 Mar 1997 19:19:09 GMT

>stuff that _resembles_ triangle. Didn't know such a formula existed.

The following is an extract from my file hopside.uue found at 
ftp://ftp.mindspring.com/pub/users/scoundrl.  This chart depicts the miter
angle 
and blade tilt for compund miter cuts as in crown mold or an inverted 
pyramid with various numbers of sides.  A right angle, for example would 
correspond to a four-sided figure, so you would look at the "4" column 
and trace down to the number of degrees of flair out from vertical.  This 
is usually 45 degrees.  

The actual chart for Excel or Quattro Pro includes a much larger number of
potential "sides" to the figure.  There is a sister-program called
hopangle.uue, which replaces the columns labeled "number of sides" with 2
degree increments of angle, including 33-1/3 and 45.  This is simply too
large to post here. 

Finally, there is a third file called hopper.uue that is a "calculator" 
where you input your change of direction or number of sides together with 
degrees of flair and read out the miter gauge and bevel settings directly.

I don't understand why I can't get the darn columns to align when I post the
file, but I think any interested person could figure the setting out from the
information below.

Tom Gauldin   [email-masked]

                 COMPOUND MITER CUT CALCULATIONS
                         NON-BEDDED CUTS
              
               ---------------------------------

                                                     NUMBER OF SIDES
                                                    3     4        5       6
etc.
                                                   ---  ---  ---  ---  ---  -
    DEGREE    2  BLADE TILT   59.9 45.0 36.0 30.0 25.7  22.5  20.0  18.0
    OF FLAIR     MITRE ANGLE   3.5  2.0  1.5  1.2  1.0   0.8   0.7   0.6
    OUT FROM  4  BLADE TILT   59.8 44.9 35.9 29.9 25.6  22.4  19.9  18.0
    VERTICAL     MITRE ANGLE   6.9  4.0  2.9  2.3  1.9   1.7   1.5   1.3
              6  BLADE TILT   59.5 44.7 35.8 29.8 25.6  22.4  19.9  17.9
                 MITRE ANGLE  10.3  6.0  4.3  3.5  2.9   2.5   2.2   1.9
              8  BLADE TILT   59.0 44.4 35.6 29.7 25.4  22.3  19.8  17.8
                 MITRE ANGLE  13.6  7.9  5.8  4.6  3.8   3.3   2.9   2.6
             10  BLADE TILT   58.5 44.1 35.4 29.5 25.3  22.1  19.7  17.7
                 MITRE ANGLE  16.7  9.9  7.2  5.7  4.8   4.1   3.6   3.2
             12  BLADE TILT   57.9 43.8 35.1 29.3 25.1  22.0  19.5  17.6
                 MITRE ANGLE  19.8 11.7  8.6  6.8  5.7   4.9   4.3   3.9
             14  BLADE TILT   57.2 43.3 34.8 29.0 24.9  21.8  19.4  17.4
                 MITRE ANGLE  22.7 13.6 10.0  8.0  6.6   5.7   5.0   4.5
             16  BLADE TILT   56.4 42.8 34.4 28.7 24.7  21.6  19.2  17.3
                 MITRE ANGLE  25.5 15.4 11.3  9.0  7.6   6.5   5.7   5.1
             18  BLADE TILT   55.5 42.3 34.0 28.4 24.4  21.3  19.0  17.1
                 MITRE ANGLE  28.2 17.2 12.7 10.1  8.5   7.3   6.4   5.7
             20  BLADE TILT   54.5 41.6 33.5 28.0 24.1  21.1  18.7  16.9
                 MITRE ANGLE  30.6 18.9 14.0 11.2  9.4   8.1   7.1   6.3
             22  BLADE TILT   53.4 41.0 33.0 27.6 23.7  20.8  18.5  16.6
                 MITRE ANGLE  33.0 20.5 15.2 12.2 10.2   8.8   7.8   6.9
             24  BLADE TILT   52.3 40.2 32.5 27.2 23.4  20.5  18.2  16.4
                 MITRE ANGLE  35.2 22.1 16.5 13.2 11.1   9.6   8.4   7.5
             26  BLADE TILT   51.1 39.5 31.9 26.7 23.0  20.1  17.9  16.1
                 MITRE ANGLE  37.2 23.7 17.7 14.2 11.9  10.3   9.1   8.1
             28  BLADE TILT   49.9 38.6 31.3 26.2 22.5  19.7  17.6  15.8
                 MITRE ANGLE  39.1 25.1 18.8 15.2 12.7  11.0   9.7   8.7
             30  BLADE TILT   48.6 37.8 30.6 25.7 22.1  19.4  17.2  15.5
                 MITRE ANGLE  40.9 26.6 20.0 16.1 13.5  11.7  10.3   9.2
             32  BLADE TILT   47.3 36.8 29.9 25.1 21.6  18.9  16.9  15.2
                 MITRE ANGLE  42.5 27.9 21.1 17.0 14.3  12.4  10.9   9.8
             33  BLADE TILT   46.6 36.4 29.5 24.8 21.3  18.7  16.7  15.0
                 MITRE ANGLE  43.3 28.6 21.6 17.5 14.7  12.7  11.2  10.0
             34  BLADE TILT   45.9 35.9 29.2 24.5 21.1  18.5  16.5  14.8
                 MITRE ANGLE  44.1 29.2 22.1 17.9 15.1  13.0  11.5  10.3
             36  BLADE TILT   44.5 34.9 28.4 23.9 20.5  18.0  16.1  14.5
                 MITRE ANGLE  45.5 30.4 23.1 18.7 15.8  13.7  12.1  10.8
             38  BLADE TILT   43.0 33.9 27.6 23.2 20.0  17.6  15.6  14.1
                 MITRE ANGLE  46.8 31.6 24.1 19.6 16.5  14.3  12.6  11.3
             40  BLADE TILT   41.6 32.8 26.8 22.5 19.4  17.0  15.2  13.7
                 MITRE ANGLE  48.1 32.7 25.0 20.4 17.2  14.9  13.2  11.8
             42  BLADE TILT   40.1 31.7 25.9 21.8 18.8  16.5  14.7  13.3
                 MITRE ANGLE  49.2 33.8 25.9 21.1 17.9  15.5  13.7  12.3
             44  BLADE TILT   38.5 30.6 25.0 21.1 18.2  16.0  14.2  12.8
                 MITRE ANGLE  50.3 34.8 26.8 21.9 18.5  16.1  14.2  12.7
             45  BLADE TILT   37.8 30.0 24.6 20.7 17.9  15.7  14.0  12.6
                 MITRE ANGLE  50.8 35.3 27.2 22.2 18.8  16.3  14.4  12.9
             46  BLADE TILT   37.0 29.4 24.1 20.3 17.5  15.4  13.7  12.4
                 MITRE ANGLE  51.2 35.7 27.6 22.6 19.1  16.6  14.7  13.2
             48  BLADE TILT   35.4 28.2 23.2 19.5 16.9  14.8  13.2  11.9
                 MITRE ANGLE  52.2 36.6 28.4 23.2 19.7  17.1  15.1  13.6
             50  BLADE TILT   33.8 27.0 22.2 18.7 16.2  14.2  12.7  11.5
                 MITRE ANGLE  53.0 37.5 29.1 23.9 20.2  17.6  15.6  14.0
             52  BLADE TILT   32.2 25.8 21.2 17.9 15.5  13.6  12.2  11.0
                 MITRE ANGLE  53.8 38.2 29.8 24.5 20.8  18.1  16.0  14.4
             54  BLADE TILT   30.6 24.6 20.2 17.1 14.8  13.0  11.6  10.5
                 MITRE ANGLE  54.5 39.0 30.4 25.0 21.3  18.5  16.4  14.7
             56  BLADE TILT   29.0 23.3 19.2 16.2 14.0  12.4  11.0  10.0
                 MITRE ANGLE  55.1 39.7 31.1 25.6 21.8  19.0  16.8  15.1
             58  BLADE TILT   27.3 22.0 18.1 15.4 13.3  11.7  10.4   9.4
                 MITRE ANGLE  55.8 40.3 31.6 26.1 22.2  19.4  17.2  15.4
             60  BLADE TILT   25.7 20.7 17.1 14.5 12.5  11.0   9.8   8.9
                 MITRE ANGLE  56.3 40.9 32.2 26.6 22.6  19.7  17.5  15.7
             62  BLADE TILT   24.0 19.4 16.0 13.6 11.8  10.3   9.2   8.3
                 MITRE ANGLE  56.8 41.4 32.7 27.0 23.0  20.1  17.8  16.0
             64  BLADE TILT   22.3 18.1 14.9 12.7 11.0   9.7   8.6   7.8
                 MITRE ANGLE  57.3 41.9 33.1 27.4 23.4  20.4  18.1  16.3
             66  BLADE TILT   20.6 16.7 13.8 11.7 10.2   9.0   8.0   7.2
                 MITRE ANGLE  57.7 42.4 33.6 27.8 23.7  20.7  18.4  16.5
             68  BLADE TILT   18.9 15.4 12.7 10.8  9.4   8.2   7.4   6.6
                 MITRE ANGLE  58.1 42.8 34.0 28.2 24.1  21.0  18.6  16.8
             70  BLADE TILT   17.2 14.0 11.6  9.8  8.5   7.5   6.7   6.1
                 MITRE ANGLE  58.4 43.2 34.3 28.5 24.3  21.3  18.9  17.0
             72  BLADE TILT   15.5 12.6 10.5  8.9  7.7   6.8   6.1   5.5
                 MITRE ANGLE  58.7 43.6 34.6 28.8 24.6  21.5  19.1  17.2
             74  BLADE TILT   13.8 11.2  9.3  7.9  6.9   6.1   5.4   4.9
                 MITRE ANGLE  59.0 43.9 34.9 29.0 24.8  21.7  19.3  17.3
             76  BLADE TILT   12.1  9.8  8.2  6.9  6.0   5.3   4.7   4.3
                 MITRE ANGLE  59.2 44.1 35.2 29.3 25.0  21.9  19.5  17.5
             78  BLADE TILT   10.4  8.5  7.0  6.0  5.2   4.6   4.1   3.7
                 MITRE ANGLE  59.4 44.4 35.4 29.5 25.2  22.1  19.6  17.6
             80  BLADE TILT    8.6  7.1  5.9  5.0  4.3   3.8   3.4   3.1
                 MITRE ANGLE  59.6 44.6 35.6 29.6 25.4  22.2  19.7  17.7
             82  BLADE TILT    6.9  5.6  4.7  4.0  3.5   3.1   2.7   2.5
                 MITRE ANGLE  59.8 44.7 35.7 29.8 25.5  22.3  19.8  17.8
             84  BLADE TILT    5.2  4.2  3.5  3.0  2.6   2.3   2.0   1.9
                 MITRE ANGLE  59.9 44.8 35.9 29.9 25.6  22.4  19.9  17.9
             86  BLADE TILT    3.5  2.8  2.3  2.0  1.7   1.5   1.4   1.2
                 MITRE ANGLE  59.9 44.9 35.9 29.9 25.7  22.5  20.0  18.0
             88  BLADE TILT    1.7  1.4  1.2  1.0  0.9   0.8   0.7   0.6
                 MITRE ANGLE  60.0 45.0 36.0 30.0 25.7  22.5  20.0  18.0
             90  BLADE TILT    0.0  0.0  0.0  0.0  0.0   0.0   0.0   0.0
                 MITRE ANGLE  60.0 45.0 36.0 30.0 25.7  22.5  20.0  18.0

                 COMPOUND MITER CUT CALCULATIONS
                         NON-BEDDED CUTS
                                        ---------------------------------
                                                     NUMBER OF SIDES
                                 3    4    5    6    7     8     9    10
                               ---  ---  ---  ---  ---  ---   ---   ---
    DEGREE    2  BLADE TILT   59.9 45.0 36.0 30.0 25.7  22.5  20.0  18.0
    OF FLAIR     MITRE ANGLE   3.5  2.0  1.5  1.2  1.0   0.8   0.7   0.6
    OUT FROM  4  BLADE TILT   59.8 44.9 35.9 29.9 25.6  22.4  19.9  18.0
    VERTICAL     MITRE ANGLE   6.9  4.0  2.9  2.3  1.9   1.7   1.5   1.3
              6  BLADE TILT   59.5 44.7 35.8 29.8 25.6  22.4  19.9  17.9
                 MITRE ANGLE  10.3  6.0  4.3  3.5  2.9   2.5   2.2   1.9
              8  BLADE TILT   59.0 44.4 35.6 29.7 25.4  22.3  19.8  17.8
                 MITRE ANGLE  13.6  7.9  5.8  4.6  3.8   3.3   2.9   2.6
             10  BLADE TILT   58.5 44.1 35.4 29.5 25.3  22.1  19.7  17.7
                 MITRE ANGLE  16.7  9.9  7.2  5.7  4.8   4.1   3.6   3.2
             12  BLADE TILT   57.9 43.8 35.1 29.3 25.1  22.0  19.5  17.6
                 MITRE ANGLE  19.8 11.7  8.6  6.8  5.7   4.9   4.3   3.9
             14  BLADE TILT   57.2 43.3 34.8 29.0 24.9  21.8  19.4  17.4
                 MITRE ANGLE  22.7 13.6 10.0  8.0  6.6   5.7   5.0   4.5
             16  BLADE TILT   56.4 42.8 34.4 28.7 24.7  21.6  19.2  17.3
                 MITRE ANGLE  25.5 15.4 11.3  9.0  7.6   6.5   5.7   5.1
             18  BLADE TILT   55.5 42.3 34.0 28.4 24.4  21.3  19.0  17.1
                 MITRE ANGLE  28.2 17.2 12.7 10.1  8.5   7.3   6.4   5.7
             20  BLADE TILT   54.5 41.6 33.5 28.0 24.1  21.1  18.7  16.9
                 MITRE ANGLE  30.6 18.9 14.0 11.2  9.4   8.1   7.1   6.3
             22  BLADE TILT   53.4 41.0 33.0 27.6 23.7  20.8  18.5  16.6
                 MITRE ANGLE  33.0 20.5 15.2 12.2 10.2   8.8   7.8   6.9
             24  BLADE TILT   52.3 40.2 32.5 27.2 23.4  20.5  18.2  16.4
                 MITRE ANGLE  35.2 22.1 16.5 13.2 11.1   9.6   8.4   7.5
             26  BLADE TILT   51.1 39.5 31.9 26.7 23.0  20.1  17.9  16.1
                 MITRE ANGLE  37.2 23.7 17.7 14.2 11.9  10.3   9.1   8.1
             28  BLADE TILT   49.9 38.6 31.3 26.2 22.5  19.7  17.6  15.8
                 MITRE ANGLE  39.1 25.1 18.8 15.2 12.7  11.0   9.7   8.7
             30  BLADE TILT   48.6 37.8 30.6 25.7 22.1  19.4  17.2  15.5
                 MITRE ANGLE  40.9 26.6 20.0 16.1 13.5  11.7  10.3   9.2
             32  BLADE TILT   47.3 36.8 29.9 25.1 21.6  18.9  16.9  15.2
                 MITRE ANGLE  42.5 27.9 21.1 17.0 14.3  12.4  10.9   9.8
             33  BLADE TILT   46.6 36.4 29.5 24.8 21.3  18.7  16.7  15.0
                 MITRE ANGLE  43.3 28.6 21.6 17.5 14.7  12.7  11.2  10.0
             34  BLADE TILT   45.9 35.9 29.2 24.5 21.1  18.5  16.5  14.8
                 MITRE ANGLE  44.1 29.2 22.1 17.9 15.1  13.0  11.5  10.3
             36  BLADE TILT   44.5 34.9 28.4 23.9 20.5  18.0  16.1  14.5
                 MITRE ANGLE  45.5 30.4 23.1 18.7 15.8  13.7  12.1  10.8
             38  BLADE TILT   43.0 33.9 27.6 23.2 20.0  17.6  15.6  14.1
                 MITRE ANGLE  46.8 31.6 24.1 19.6 16.5  14.3  12.6  11.3
             40  BLADE TILT   41.6 32.8 26.8 22.5 19.4  17.0  15.2  13.7
                 MITRE ANGLE  48.1 32.7 25.0 20.4 17.2  14.9  13.2  11.8
             42  BLADE TILT   40.1 31.7 25.9 21.8 18.8  16.5  14.7  13.3
                 MITRE ANGLE  49.2 33.8 25.9 21.1 17.9  15.5  13.7  12.3
             44  BLADE TILT   38.5 30.6 25.0 21.1 18.2  16.0  14.2  12.8
                 MITRE ANGLE  50.3 34.8 26.8 21.9 18.5  16.1  14.2  12.7
             45  BLADE TILT   37.8 30.0 24.6 20.7 17.9  15.7  14.0  12.6
                 MITRE ANGLE  50.8 35.3 27.2 22.2 18.8  16.3  14.4  12.9
             46  BLADE TILT   37.0 29.4 24.1 20.3 17.5  15.4  13.7  12.4
                 MITRE ANGLE  51.2 35.7 27.6 22.6 19.1  16.6  14.7  13.2
             48  BLADE TILT   35.4 28.2 23.2 19.5 16.9  14.8  13.2  11.9
                 MITRE ANGLE  52.2 36.6 28.4 23.2 19.7  17.1  15.1  13.6
             50  BLADE TILT   33.8 27.0 22.2 18.7 16.2  14.2  12.7  11.5
                 MITRE ANGLE  53.0 37.5 29.1 23.9 20.2  17.6  15.6  14.0
             52  BLADE TILT   32.2 25.8 21.2 17.9 15.5  13.6  12.2  11.0
                 MITRE ANGLE  53.8 38.2 29.8 24.5 20.8  18.1  16.0  14.4
             54  BLADE TILT   30.6 24.6 20.2 17.1 14.8  13.0  11.6  10.5
                 MITRE ANGLE  54.5 39.0 30.4 25.0 21.3  18.5  16.4  14.7
             56  BLADE TILT   29.0 23.3 19.2 16.2 14.0  12.4  11.0  10.0
                 MITRE ANGLE  55.1 39.7 31.1 25.6 21.8  19.0  16.8  15.1
             58  BLADE TILT   27.3 22.0 18.1 15.4 13.3  11.7  10.4   9.4
                 MITRE ANGLE  55.8 40.3 31.6 26.1 22.2  19.4  17.2  15.4
             60  BLADE TILT   25.7 20.7 17.1 14.5 12.5  11.0   9.8   8.9
                 MITRE ANGLE  56.3 40.9 32.2 26.6 22.6  19.7  17.5  15.7
             62  BLADE TILT   24.0 19.4 16.0 13.6 11.8  10.3   9.2   8.3
                 MITRE ANGLE  56.8 41.4 32.7 27.0 23.0  20.1  17.8  16.0
             64  BLADE TILT   22.3 18.1 14.9 12.7 11.0   9.7   8.6   7.8
                 MITRE ANGLE  57.3 41.9 33.1 27.4 23.4  20.4  18.1  16.3
             66  BLADE TILT   20.6 16.7 13.8 11.7 10.2   9.0   8.0   7.2
                 MITRE ANGLE  57.7 42.4 33.6 27.8 23.7  20.7  18.4  16.5
             68  BLADE TILT   18.9 15.4 12.7 10.8  9.4   8.2   7.4   6.6
                 MITRE ANGLE  58.1 42.8 34.0 28.2 24.1  21.0  18.6  16.8
             70  BLADE TILT   17.2 14.0 11.6  9.8  8.5   7.5   6.7   6.1
                 MITRE ANGLE  58.4 43.2 34.3 28.5 24.3  21.3  18.9  17.0
             72  BLADE TILT   15.5 12.6 10.5  8.9  7.7   6.8   6.1   5.5
                 MITRE ANGLE  58.7 43.6 34.6 28.8 24.6  21.5  19.1  17.2
             74  BLADE TILT   13.8 11.2  9.3  7.9  6.9   6.1   5.4   4.9
                 MITRE ANGLE  59.0 43.9 34.9 29.0 24.8  21.7  19.3  17.3
             76  BLADE TILT   12.1  9.8  8.2  6.9  6.0   5.3   4.7   4.3
                 MITRE ANGLE  59.2 44.1 35.2 29.3 25.0  21.9  19.5  17.5
             78  BLADE TILT   10.4  8.5  7.0  6.0  5.2   4.6   4.1   3.7
                 MITRE ANGLE  59.4 44.4 35.4 29.5 25.2  22.1  19.6  17.6
             80  BLADE TILT    8.6  7.1  5.9  5.0  4.3   3.8   3.4   3.1
                 MITRE ANGLE  59.6 44.6 35.6 29.6 25.4  22.2  19.7  17.7
             82  BLADE TILT    6.9  5.6  4.7  4.0  3.5   3.1   2.7   2.5
                 MITRE ANGLE  59.8 44.7 35.7 29.8 25.5  22.3  19.8  17.8
             84  BLADE TILT    5.2  4.2  3.5  3.0  2.6   2.3   2.0   1.9
                 MITRE ANGLE  59.9 44.8 35.9 29.9 25.6  22.4  19.9  17.9
             86  BLADE TILT    3.5  2.8  2.3  2.0  1.7   1.5   1.4   1.2
                 MITRE ANGLE  59.9 44.9 35.9 29.9 25.7  22.5  20.0  18.0
             88  BLADE TILT    1.7  1.4  1.2  1.0  0.9   0.8   0.7   0.6
                 MITRE ANGLE  60.0 45.0 36.0 30.0 25.7  22.5  20.0  18.0
             90  BLADE TILT    0.0  0.0  0.0  0.0  0.0   0.0   0.0   0.0
                 MITRE ANGLE  60.0 45.0 36.0 30.0 25.7  22.5  20.0  18.0