I've got a board set at a 45 degree angle, back from a line. How much
(percentage) of the length of the board does it take up? To
conceptualize the issue, I drew a one inch line on paper with a ruler,
and rotated the ruler to a 45 degree angle, thinking that the one inch
mark on the ruler would be only 1/2 away from the starting point (along
the original path of the ruler), but it looks like it's about 90% along
the one inch span. What's the formula?

Dave

Hope the ASCII art is legible...

.707"
|---|

/
/
/ 45 deg angle
/_______

|- 1" -|

The length of the diagonal line is 1".

The diagonal of a 1" square is 1.414"

--
JeffB
remove no.spam. to email


David wrote:
I've got a board set at a 45 degree angle, back from a line. How much
(percentage) of the length of the board does it take up? To
conceptualize the issue, I drew a one inch line on paper with a ruler,
and rotated the ruler to a 45 degree angle, thinking that the one inch
mark on the ruler would be only 1/2 away from the starting point (along
the original path of the ruler), but it looks like it's about 90% along
the one inch span. What's the formula?

Dave

Jeff, I laid the ruler out again and it still looks like it's close to
85% or so. I place the ruler in front of me, on paper, and then pivot
it about the zero mark (at the left end). The I look to see how far
along the original line the 1" mark is and it looks to be over 85% along
that path, if I draw a line straight down from the 1" mark to the
original path line. The triangle that would result is an isosceles
triangle with 2ea 1 inch sides. But then I can't figure out how to
determine where a line between one of the equal angles and the opposite
equal length line, would intersect (that would give me the distance that
I'm looking for).

Dave

JeffB wrote:

Hope the ASCII art is legible...

.707"
|---|

/
/
/ 45 deg angle
/_______

|- 1" -|

The length of the diagonal line is 1".

The diagonal of a 1" square is 1.414"

On Mon, 11 Apr 2005 10:50:59 -0700, David wrote:

Jeff, I laid the ruler out again and it still looks like it's close to
85% or so. I place the ruler in front of me, on paper, and then pivot
it about the zero mark (at the left end). The I look to see how far
along the original line the 1" mark is and it looks to be over 85% along
that path, if I draw a line straight down from the 1" mark to the
original path line. The triangle that would result is an isosceles
triangle with 2ea 1 inch sides. But then I can't figure out how to
determine where a line between one of the equal angles and the opposite
equal length line, would intersect (that would give me the distance that
I'm looking for).

I'll admit, I'm having a little trouble following exactly what you are
describing, but are you looking for the standard trig formulas?

Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

If you know what your angle between the two 1" lines is, you should be
able to get the appropriate angle value (Sin, Cos, or Tan) from a
decent scientific calculator or a Trig table, and then just use
standard algebra rules to solve for your missing dimention.
Aut inveniam viam aut faciam

Forget my last post. NOW i see my mistake: I eyeballed the 45 degree
angle wrong--I had it a bit less than 45. It's as you said.

Now I can start cutting some wood! Thanks, Jeff


Dave

JeffB wrote:

Hope the ASCII art is legible...

.707"
|---|

/
/
/ 45 deg angle
/_______

|- 1" -|

The length of the diagonal line is 1".

The diagonal of a 1" square is 1.414"

If you mean a miter cut, the length of the miter is

the root of two times the square of the width of the board.

If you mean a bevel cut, the length of the bevel is

the root of two times the square of the thickness of the board.

1 inch wide =3D 1.4142135623730950488016887242097
2 inch wide =3D 2.8284271247461900976033774484194
3 inch wide =3D 4.24264068711928514640506617262909
4 inch wide =3D 5.65685424949238019520675489683879

It appears the bevel/miter is proportional to the width by a factor of =
~1.41.
Or, the width/thickness is always 70.7106781186547524400844362105198% of =
the bevel/miter.

--=20

PDQ
--
=20
"David" wrote in message =
...
| I've got a board set at a 45 degree angle, back from a line. How much =

| (percentage) of the length of the board does it take up? To=20
| conceptualize the issue, I drew a one inch line on paper with a ruler, =

| and rotated the ruler to a 45 degree angle, thinking that the one inch =

| mark on the ruler would be only 1/2 away from the starting point =
(along=20
| the original path of the ruler), but it looks like it's about 90% =
along=20
| the one inch span. What's the formula?
|=20
| Dave

In article , "PDQ" wrote:
If you mean a miter cut, the length of the miter is

the root of two times the square of the width of the board.

Try again. Square root of 2 times the width of the board _not_ squared.

If you mean a bevel cut, the length of the bevel is

the root of two times the square of the thickness of the board.

Try again. Square root of 2 times the thickness of the board _not_ squared.
Your formulas below are correct (even though given with an absurd degree of
precision), but your descriptions above are wrong, and don't match the
formulas.

1 inch wide = 1.4142135623730950488016887242097
2 inch wide = 2.8284271247461900976033774484194
3 inch wide = 4.24264068711928514640506617262909
4 inch wide = 5.65685424949238019520675489683879

It appears the bevel/miter is proportional to the width by a factor of =
~1.41.

Yes. Proportional to the width. Not to the square of the width.

Or, the width/thickness is always 70.7106781186547524400844362105198% of
the bevel/miter.

70.7 % is plenty close enough.

--
Regards,
Doug Miller (alphageek at milmac dot com)

Nobody ever left footprints in the sands of time by sitting on his butt.
And who wants to leave buttprints in the sands of time?

Picky, picky, picky.

If you want to play those games, Doug:

"Bevel" is described as "the angle formed at the juncture of two non =
perpendicular surfaces."

"Miter" could mean "a tall ornamental liturgical headdress" worn by some =
members of the clergy, or it could mean, as it does in this case, =
"either of the surfaces that come together in a miter joint".

If you want to play with polygonal surfaces, why not say so? "board =
_not_ squared" is so imprecise.

I guess your problem must lie with your inability to visualize the =
position of the board within its frame of reference.

I am further amazed that one who would advertise one's self as a "Geek" =
would be unable to appreciate the intended absurdity of the precision. =
I was leaving it up the positor, to extract a suitable level of =
imprecision.

Go play with your semantics, sirrah.=20

--=20

PDQ
--
=20
"Doug Miller" wrote in message =
. ..
| In article , "PDQ" =
wrote:
| If you mean a miter cut, the length of the miter is
|
| the root of two times the square of the width of the board.
|=20
| Try again. Square root of 2 times the width of the board _not_ =
squared.
|
| If you mean a bevel cut, the length of the bevel is
|
| the root of two times the square of the thickness of the board.
|=20
| Try again. Square root of 2 times the thickness of the board _not_ =
squared.
| Your formulas below are correct (even though given with an absurd =
degree of=20
| precision), but your descriptions above are wrong, and don't match the =

| formulas.
|
| 1 inch wide =3D 1.4142135623730950488016887242097
| 2 inch wide =3D 2.8284271247461900976033774484194
| 3 inch wide =3D 4.24264068711928514640506617262909
| 4 inch wide =3D 5.65685424949238019520675489683879
|
| It appears the bevel/miter is proportional to the width by a factor =
of =3D
| ~1.41.
|=20
| Yes. Proportional to the width. Not to the square of the width.
|=20
| Or, the width/thickness is always 70.7106781186547524400844362105198% =
of=20
| the bevel/miter.
|=20
| 70.7 % is plenty close enough.
|=20
| --
| Regards,
| Doug Miller (alphageek at milmac dot com)
|=20
| Nobody ever left footprints in the sands of time by sitting on his =
butt.
| And who wants to leave buttprints in the sands of time?

In article , "PDQ" wrote:
Picky, picky, picky.

If you want to play those games, Doug:

"Bevel" is described as "the angle formed at the juncture of two non =
perpendicular surfaces."

"Miter" could mean "a tall ornamental liturgical headdress" worn by some =
members of the clergy, or it could mean, as it does in this case, =
"either of the surfaces that come together in a miter joint".

If you want to play with polygonal surfaces, why not say so? "board =
_not_ squared" is so imprecise.

I guess your problem must lie with your inability to visualize the =
position of the board within its frame of reference.

You missed the point rather dramatically, I'm afraid. You wrote that the width
of the miter was proportional to "the square of the width of the board".

This is false.

It is proportional to the *width* of the board. Period. Not the square of its
width.

You then compounded this error by repeating it with respect to thickness, and
bevels.

And now you've compounded it still further by showing that, in addition to
your difficulties with mathematics, you also have some reading comprehension
issues.

--
Regards,
Doug Miller (alphageek at milmac dot com)

Nobody ever left footprints in the sands of time by sitting on his butt.
And who wants to leave buttprints in the sands of time?

If you mean a miter cut, the length of the miter is

the root of two times the square of the width of the board.

If you mean a bevel cut, the length of the bevel is

the root of two times the square of the thickness of the board.

1 inch wide =3D 1.4142135623730950488016887242097
2 inch wide =3D 2.8284271247461900976033774484194
3 inch wide =3D 4.24264068711928514640506617262909
4 inch wide =3D 5.65685424949238019520675489683879

It appears the bevel/miter is proportional to the width by a factor of =
~1.41.
Or, the width/thickness is always 70.7106781186547524400844362105198% of =
the bevel/miter.
__________________________________________________ _______

Dougie, you said

| You missed the point rather dramatically, I'm afraid. You wrote that =
the width=20
| of the miter was proportional to "the square of the width of the =
board".=20

I don't think so. No where in the preceding, which I include herewith =
for clarity, did I state what you saw.

Better get your eyes checked. Your geekiness leaves much to be desired. =
You might, however, be in line for the "Conehead" awards.
__________________________________________________ ______
--=20

PDQ
--
=20
"David" wrote in message =
...
| I've got a board set at a 45 degree angle, back from a line. How much =

| (percentage) of the length of the board does it take up? To=20
| conceptualize the issue, I drew a one inch line on paper with a ruler, =

| and rotated the ruler to a 45 degree angle, thinking that the one inch =

| mark on the ruler would be only 1/2 away from the starting point =
(along=20
| the original path of the ruler), but it looks like it's about 90% =
along=20
| the one inch span. What's the formula?
|=20
| Dave

--=20

PDQ
--
=20
"Doug Miller" wrote in message =
. ..
| In article , "PDQ" =
wrote:
| Picky, picky, picky.
|
| If you want to play those games, Doug:
|
| "Bevel" is described as "the angle formed at the juncture of two non =
=3D
| perpendicular surfaces."
|
| "Miter" could mean "a tall ornamental liturgical headdress" worn by =
some =3D
| members of the clergy, or it could mean, as it does in this case, =3D
| "either of the surfaces that come together in a miter joint".
|
| If you want to play with polygonal surfaces, why not say so? "board =
=3D
| _not_ squared" is so imprecise.
|
| I guess your problem must lie with your inability to visualize the =
=3D
| position of the board within its frame of reference.
|=20
| You missed the point rather dramatically, I'm afraid. You wrote that =
the width=20
| of the miter was proportional to "the square of the width of the =
board".=20
|=20
| This is false.
|=20
| It is proportional to the *width* of the board. Period. Not the square =
of its=20
| width.
|=20
| You then compounded this error by repeating it with respect to =
thickness, and=20
| bevels.
|=20
| And now you've compounded it still further by showing that, in =
addition to=20
| your difficulties with mathematics, you also have some reading =
comprehension=20
| issues.
|=20
| --
| Regards,
| Doug Miller (alphageek at milmac dot com)
|=20
| Nobody ever left footprints in the sands of time by sitting on his =
butt.
| And who wants to leave buttprints in the sands of time?

"Doug Miller" wrote in message
. ..
In article , "PDQ"
wrote:
If you mean a miter cut, the length of the miter is

the root of two times the square of the width of the board.

Try again. Square root of 2 times the width of the board _not_ squared.

If you mean a bevel cut, the length of the bevel is

the root of two times the square of the thickness of the board.

Try again. Square root of 2 times the thickness of the board _not_
squared.
Your formulas below are correct (even though given with an absurd degree
of
precision), but your descriptions above are wrong, and don't match the
formulas.

1 inch wide = 1.4142135623730950488016887242097
2 inch wide = 2.8284271247461900976033774484194
3 inch wide = 4.24264068711928514640506617262909
4 inch wide = 5.65685424949238019520675489683879

It appears the bevel/miter is proportional to the width by a factor of =
~1.41.

Yes. Proportional to the width. Not to the square of the width.

Or, the width/thickness is always 70.7106781186547524400844362105198% of
the bevel/miter.

I find measuring to 20 decimal places is usually good enough for me.
Although I only make things like garden furniture and planters etc.

Oldun

You gotta go that deep to see how much your IRS refund is.

Other than then, who cares for more than a silly millimeter?

--=20

PDQ
--
=20
"Oldun" wrote in message =
...
|=20
| "Doug Miller" wrote in message=20
| . ..
| In article , "PDQ"=20
| wrote:
| If you mean a miter cut, the length of the miter is
|
| the root of two times the square of the width of the board.
|
| Try again. Square root of 2 times the width of the board _not_ =
squared.
|
| If you mean a bevel cut, the length of the bevel is
|
| the root of two times the square of the thickness of the board.
|
| Try again. Square root of 2 times the thickness of the board _not_=20
| squared.
| Your formulas below are correct (even though given with an absurd =
degree=20
| of
| precision), but your descriptions above are wrong, and don't match =
the
| formulas.
|
| 1 inch wide =3D 1.4142135623730950488016887242097
| 2 inch wide =3D 2.8284271247461900976033774484194
| 3 inch wide =3D 4.24264068711928514640506617262909
| 4 inch wide =3D 5.65685424949238019520675489683879
|
| It appears the bevel/miter is proportional to the width by a factor =
of =3D
| ~1.41.
|
| Yes. Proportional to the width. Not to the square of the width.
|
| Or, the width/thickness is always =
70.7106781186547524400844362105198% of
| the bevel/miter.
|
| I find measuring to 20 decimal places is usually good enough for me.=20
| Although I only make things like garden furniture and planters etc.
|=20
| Oldun=20
|=20
|

On Mon, 11 Apr 2005 14:03:11 -0400, "PDQ" wrote
something
.......and in reply I say!:

the root of two times the square of the thickness of the board.

Which I immediately read as "1.414 * thickness * thickness". I would
have to gnash quite a bit before I was happy that I had it right or
wrong.

Amongst all your arguing, I think it would have made matters a damned
sight easier if you had used a few brackets to clear things up right
at the start, or rephrased your statement.

You were replying to someone, who was asking about a very fundamental
geometry question, in a way guaranteed to provide abiguity to all but
the "inner circle" of your conventions of math and English.

Subsequent replies from you indicate that basically you were being a
smartarse.

All you had to say was "the square root of (two times (the square of
the thickness of the board))".

or even (sqrt(2*(thickness ^2))"

************************************************** ****************************************
WHY _ARE_ WE HERE?

Nick White --- HEAD:Hertz Music

remove ns from my header address to reply via email

!!
")
_/ )
( )
_//- \__/

David wrote:

I've got a board set at a 45 degree angle, back from a line. How much
(percentage) of the length of the board does it take up? To
conceptualize the issue, I drew a one inch line on paper with a ruler,
and rotated the ruler to a 45 degree angle, thinking that the one inch
mark on the ruler would be only 1/2 away from the starting point (along
the original path of the ruler), but it looks like it's about 90% along
the one inch span. What's the formula?

Dave
If you make a 90 deg. angle of two lines of the same length,
a line connecting the two other ends is 45 degrees at each
end.
Trivia: The check the accuracy of a 90 deg. angle, measure 3
units (inches, yards, feet, etc) along one side and 4 units
along the other. The two marks will be 5 units apart. Saw a
cabinet maker use this and he had never heard of hypotenuse.

Further trivia: If you put 12 equally spaced knots or marks
in a circle of string and have three persons holding knot
#1, #5 and #8 respectively and pull all three sides taut, it
will make a 90 degree angle at knot #5.

--
Gerald Ross
Cochran, GA

If it's worth doing, it's worth doing
for money.





----== Posted via Newsfeeds.Com - Unlimited-Uncensored-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
----= East and West-Coast Server Farms - Total Privacy via Encryption =----

Further trivia: If you put 12 equally spaced knots or marks
in a circle of string and have three persons holding knot
#1, #5 and #8 respectively and pull all three sides taut, it
will make a 90 degree angle at knot #5.

Interesting, I never heard that one. Euclid's method is to take any
point on a circle, and then draw line from that point to the points
where any diameter crosses the circle. The resulting angle will
always be 90 degrees.
Aut inveniam viam aut faciam

In article ,
Prometheus wrote:

Further trivia: If you put 12 equally spaced knots or marks
in a circle of string and have three persons holding knot
#1, #5 and #8 respectively and pull all three sides taut, it
will make a 90 degree angle at knot #5.

Interesting, I never heard that one.

Guess what you get when you add 3, 4, and 5 ? grin

Euclid's method is to take any
point on a circle, and then draw line from that point to the points
where any diameter crosses the circle. The resulting angle will
always be 90 degrees.
Aut inveniam viam aut faciam

Thanks all. I'm about to make the cuts now. 'preciate the help.

Dave

David wrote:

I've got a board set at a 45 degree angle, back from a line. How much
(percentage) of the length of the board does it take up? To
conceptualize the issue, I drew a one inch line on paper with a ruler,
and rotated the ruler to a 45 degree angle, thinking that the one inch
mark on the ruler would be only 1/2 away from the starting point (along
the original path of the ruler), but it looks like it's about 90% along
the one inch span. What's the formula?

Dave

On Mon, 11 Apr 2005 10:27:33 -0700, David wrote:

I've got a board set at a 45 degree angle, back from a line. How much
(percentage) of the length of the board does it take up? To
conceptualize the issue, I drew a one inch line on paper with a ruler,
and rotated the ruler to a 45 degree angle, thinking that the one inch
mark on the ruler would be only 1/2 away from the starting point (along
the original path of the ruler), but it looks like it's about 90% along
the one inch span. What's the formula?

The length along the line is 1/sqrt(2) = sqrt(2)/2. As a percentage
of 1 that's 100*(sqrt(2)/2)% or 50*sqrt(2)% ~ 71%.

"D" =3D=3D "claimed thusly:

D I've got a board set at a 45 degree angle, back from a line. How much=
=20
D (percentage) of the length of the board does it take up? To=20
D conceptualize the issue, I drew a one inch line on paper with a ruler,=
=20
D and rotated the ruler to a 45 degree angle, thinking that the one inch=
=20
D mark on the ruler would be only 1/2 away from the starting point=
(along=20
D the original path of the ruler), but it looks like it's about 90%=
along=20
D the one inch span. What's the formula?

however wide the board is, that's the length which will be
removed. a 45deg triangle's two legs are equal, and the
hypotenuse is 1.4 times longer.

remember "soh-cah-toa":

sin (angle) =3D opposite / hypotenuse
cos (angle) =3D adjacent / hypotenuse
tangent (angle) =3D opposite / adjacent

also, for right triangles, the sum of the square of the sides
equals the square of the hypotenuse. that is, a^2 + b^2 =3D c^2.

i have a page for compound miters on my website, if you're at all
interested in how to use simple geometry in the shop.


regards,
greg (non-hyphenated american)
--=20

Multiculturalism is a euphemism for national division

http://users.adelphia.net/~kimnach http://www.grc.nasa.gov

I opted for Betamax, the world for VHS;=20
I for Amiga, the world IBM clones.

Esk=FCsz=FCnk, Esk=FCsz=FCnk, hogy rabok tov=E1bb nem lesz=FCnk!