Forgot my geometry...

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

{ *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]

In article <[email protected]>,
PDQ <[email protected]> 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.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>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 = 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.
>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
>| of the miter was proportional to "the square of the width of the board".
>
>I don't think so. No where in the preceding, which I include herewith
>for clarity, did I state what you saw.

Actually, you *did*. And you even quoted those _exact_words_, above.
"For clarity", the occurrences of the indicated words have been marked,
so that the vision-impaired can locate them.


>Better get your eyes checked. Your geekiness leaves much to be desired.

"Speak for yourself, John" would seem to apply.

>You might, however, be in line for the "Conehead" awards.

You're the leading candidate for the pseudo-"Ronald McDonald" award.
(The one named for the _original_ 'big red hair' circus entertainer, made
Famous by Larry Harmon.)

In article <[email protected]>,
PDQ <[email protected]> wrote:
>Guess you never pretended to be logical.
>
>I said root(2(width*width)).


Bzzzt! Thank you for playing.

That may have been what you _intended_ to say (I'll not speculate on *that*),
but it is *not* what you actually wrote.
You wrote the English words for "root(2) * width*width"

"root" is a 'higher priority' "operator" than 'times', and the associativity
is left-to-right.

Given that what you wrote above is what you actually intended to say
originally, you omitted a critical phrase from your scrivening. The words
"the quantity" was required after 'root of"

>
>My professors told me that, in the parlance, root equates to square
>root. It is just a convenient form thereof.

No argument on _that_ point.

Did your professors bother to teach you about "reduction" to simplest form?

Did your professors not teach you how *stupid* it is to do two multiplies
and a (calculated) square-root when the exact same result can be obtained
via a single multiply of a constant

>Assuming you can comprehend the above, your underscore, via a caret, is
>the same. I only wish I had a proper symbol on this pig.

Tell me, just how would you express _in_words_, "root(2) * (width*width)"
then?

>"Robert Bonomi" <[email protected]> wrote in message
>news:[email protected]...
>| { *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]
>|
>| In article <[email protected]>,
>| PDQ <[email protected]> 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.
>| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>| >
>| >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 = 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.
>| >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
>| >| of the miter was proportional to "the square of the width of the board".
>| >
>| >I don't think so. No where in the preceding, which I include herewith
>| >for clarity, did I state what you saw.
>|
>| Actually, you *did*. And you even quoted those _exact_words_, above.
>| "For clarity", the occurrences of the indicated words have been marked,
>| so that the vision-impaired can locate them.
>|
>|
>| >Better get your eyes checked. Your geekiness leaves much to be desired.
>|
>| "Speak for yourself, John" would seem to apply.
>|
>| >You might, however, be in line for the "Conehead" awards.
>|
>| You're the leading candidate for the pseudo-"Ronald McDonald" award.
>| (The one named for the _original_ 'big red hair' circus entertainer, made
>| Famous by Larry Harmon.)
>|

In article <[email protected]>,
PDQ <[email protected]> wrote:
>This is more fun that actually applying myself to wood.
>
>Have you never given any thought to the order of qualification inherent
>in the utilization of "of"?


Repeating (since you failed to address it last time):

Tell me, just how would you express _in_words_, "root(2) * (width*width)"
then?

>
>The resultant of any number multiplied by itself is the square of that number.

Repeating (since you failed to address it last time):

Did your professors bother to teach you about "reduction" to simplest form?

Did your professors not teach you how *stupid* it is to do two multiplies
and a (calculated) square-root when the exact same result can be obtained
via a single multiply of a constant

>
>ergo: miter length = root (two(thickness squared)) .

yup. "Root of the quantity two times the square of the width of the board"

>
>Amazing what is lost as a result of the "whole language" system.
>
>--
>
>PDQ
>--
>
>"Robert Bonomi" <[email protected]> wrote in message
>news:[email protected]...
>| In article <[email protected]>,
>| PDQ <[email protected]> wrote:
>| >Guess you never pretended to be logical.
>| >
>| >I said root(2(width*width)).
>|
>|
>| Bzzzt! Thank you for playing.
>|
>| That may have been what you _intended_ to say (I'll not speculate on *that*),
>| but it is *not* what you actually wrote.
>| You wrote the English words for "root(2) * width*width"
>|
>| "root" is a 'higher priority' "operator" than 'times', and the associativity
>| is left-to-right.
>|
>| Given that what you wrote above is what you actually intended to say
>| originally, you omitted a critical phrase from your scrivening. The words
>| "the quantity" was required after 'root of"
>|
>| >
>| >My professors told me that, in the parlance, root equates to square
>| >root. It is just a convenient form thereof.
>|
>| No argument on _that_ point.
>|
>| Did your professors bother to teach you about "reduction" to simplest form?
>|
>| Did your professors not teach you how *stupid* it is to do two multiplies
>| and a (calculated) square-root when the exact same result can be obtained
>| via a single multiply of a constant
>|
>| >Assuming you can comprehend the above, your underscore, via a caret, is
>| >the same. I only wish I had a proper symbol on this pig.
>|
>| Tell me, just how would you express _in_words_, "root(2) * (width*width)"
>| then?
>|
>| >"Robert Bonomi" <[email protected]> wrote in message
>| >news:[email protected]...
>| >| { *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]
>| >|
>| >| In article <[email protected]>,
>| >| PDQ <[email protected]> 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.
>| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>| >| >
>| >| >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 = 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.
>| >| >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
>| >| >| of the miter was proportional to "the square of the width of the
>board".
>| >| >
>| >| >I don't think so. No where in the preceding, which I include herewith
>| >| >for clarity, did I state what you saw.
>| >|
>| >| Actually, you *did*. And you even quoted those _exact_words_, above.
>| >| "For clarity", the occurrences of the indicated words have been marked,
>| >| so that the vision-impaired can locate them.
>| >|
>| >|
>| >| >Better get your eyes checked. Your geekiness leaves much to be desired.
>| >|
>| >| "Speak for yourself, John" would seem to apply.
>| >|
>| >| >You might, however, be in line for the "Conehead" awards.
>| >|
>| >| You're the leading candidate for the pseudo-"Ronald McDonald" award.
>| >| (The one named for the _original_ 'big red hair' circus entertainer, made
>| >| Famous by Larry Harmon.)
>| >|
>|
>|

In article <[email protected]>,
Prometheus <[email protected]> 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

Guess you never pretended to be logical.

I said root(2(width*width)).

My professors told me that, in the parlance, root equates to square =
root. It is just a convenient form thereof.

Assuming you can comprehend the above, your underscore, via a caret, is =
the same. I only wish I had a proper symbol on this pig.

--=20

PDQ
--
=20
"Robert Bonomi" <[email protected]> wrote in message =
news:[email protected]...
| { *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]
|=20
| In article <[email protected]>,
| PDQ <[email protected]> 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.
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| >
| >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.
|=20
| Actually, you *did*. And you even quoted those _exact_words_, above.
| "For clarity", the occurrences of the indicated words have been =
marked,
| so that the vision-impaired can locate them.
|=20
|=20
| >Better get your eyes checked. Your geekiness leaves much to be =
desired.
|=20
| "Speak for yourself, John" would seem to apply.
|=20
| >You might, however, be in line for the "Conehead" awards.
|=20
| You're the leading candidate for the pseudo-"Ronald McDonald" award.
| (The one named for the _original_ 'big red hair' circus entertainer, =
made
| Famous by Larry Harmon.)
|

On Tue, 12 Apr 2005 22:51:22 +0100, Andy Dingley
<[email protected]> wrote:

>On Tue, 12 Apr 2005 19:54:21 GMT, Charles Krug
><[email protected]> wrote:
>
>>Calculus--that stuff with differentials and integrals you might have hit in college.
>
>College ? Don't you guys do this in secondary school?
>(about age 13/14 ?)

I was 16 when I got to take calculus- and that was a year early, with
a recommendation from the head of the math departement. There was no
course higher than calc offered. Shame to say that in the three year
gap between that and when I took calculus 2 in college, I forgot
pretty much everything I had learned, and it really sort of soured my
taste for higher maths.

Horray for the American public education system!


Aut inveniam viam aut faciam

On Wed, 13 Apr 2005 12:04:36 -0500, Hax Planx <[email protected]> wrote:
>
> I don't think Calc needs to be a high school class. If high schoolers
> leave with a good knowledge of algebra, geometry and trigonometry they
> will be very, very well prepared for college. When some graduates can't
> find the USA on a globe, they have far bigger fish to fry.

Um. The ones taking calculus in high school, aren't the same ones who
can't find things on a globe, they're the ones who are majoring in
Phy-Ed (or whatever it's called now) and _beating up_ the ones in the
calculus class.

Hax Planx wrote:
...
> My first semester calc instructor told us on day one there would be no
> curve, even if it meant failing everybody. ...

The notorious one for that when I was an undergrad was Atomic Physics
lecture...each quiz was four problems, each counted 1/4-th, each was
right or wrong--down to specific precision for those w/ numeric
results. A real pita w/ a slide rule, for sure... :(

Dr. Livesay, the ex-Marine drill sargeant was the ogre for Analytic
Geometry (Calc IV) similar to your description...

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 =----

"Doug Miller" <[email protected]> wrote in message
news:[email protected]...
> In article <[email protected]>, "PDQ"
> <[email protected]> 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

On Mon, 11 Apr 2005 14:03:11 -0400, "PDQ" <[email protected]> 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

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

In article <[email protected]>, "PDQ" <[email protected]> wrote:
>Guess you never pretended to be logical.
>
>I said root(2(width*width)).

You said:
"the root of two times the square of the width of the board."

This has a precise meaning, to wit: [ sqrt(2) ] * [ width^2 ]

>My professors told me that, in the parlance, root equates to square
>root. It is just a convenient form thereof.

Yes, everybody understands that. Too bad you slept through the class where
they discussed precedence of operators.
>
>Assuming you can comprehend the above, your underscore, via a caret, is
>the same. I only wish I had a proper symbol on this pig.

The only comprehension problems are on your end of the line.

--
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?

=20
"Robert Bonomi" <[email protected]> wrote in message =
news:[email protected]...
| In article <[email protected]>,
| PDQ <[email protected]> wrote:
| >This is more fun that actually applying myself to wood.
| >
| >Have you never given any thought to the order of qualification =
inherent
| >in the utilization of "of"?
|=20
|=20
| Repeating (since you failed to address it last time):
| =20
| Tell me, just how would you express _in_words_, "root(2) * =
(width*width)"
| then?
| =20
Just for you: root two times width squared.
No "of", just processing.=20
1) do what's left of the "times"
2) do what's right of the "times"
3) multiply the two results together.

--=20

PDQ
--

Analytical geometry/spherical trig: I think that was the name of the
only college course I couldn't pass... (I did great in algebra, though!)

Dave

Charles Krug wrote:

>>PDQ says...
>>
>>This is more fun that actually applying myself to wood.
>>
>>Have you never given any thought to the order of qualification
>>inherent in the utilization of "of"?
>>
>
>
> Geometry is proveable. I took a course where we began with Peano's
> postulates and from that derrived all of elementary Calculus--that stuff
> with differentials and integrals you might have hit in college.
>
> It took two semesters and was BRUTAL.
>
> Lemme see if I remember . . .
>
> There is a number Zero
>
> (MANY things snipped)
>
> . . . which proves that the limit exists about a point x0.
>
> Easy peasy.
>

In article <[email protected]>, "PDQ" <[email protected]> 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?

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

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" <[email protected]> wrote in message =
news:[email protected]...
| 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" <[email protected]> wrote in message =
news:[email protected]...
| In article <[email protected]>, "PDQ" =
<[email protected]> 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?

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" <[email protected]> wrote in message =
news:[email protected]...
|=20
| "Doug Miller" <[email protected]> wrote in message=20
| news:[email protected]...
| > In article <[email protected]>, "PDQ"=20
| > <[email protected]> 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
|

=20
"BadgerDog" <[email protected]> wrote in message =
news:[email protected]...
| PDQ, to be consistent with your first post, you should use:
| ergo: miter length =3D root (two(width squared))
| OR
| ergo: bevel length =3D root (two(thickness squared))
|=20
| Sorry, given how the thread was going I couldn't help myself.
|=20
| BadgerDog
|=20
|=20
Some days one just can't seem to do more than survive.=20
By the time I got to this point, I almost didn't even care how the board =
was positioned.

Andy Dingley <[email protected]> writes:
>On Tue, 12 Apr 2005 19:54:21 GMT, Charles Krug
><[email protected]> wrote:
>
>>Calculus--that stuff with differentials and integrals you might have hit in college.
>
>College ? Don't you guys do this in secondary school?
>(about age 13/14 ?)
>

Some do. Most don't. Modern schools no longer place any emphasis on
learning - they are just socialization vehicles.

scott

PDQ says...

> This is more fun that actually applying myself to wood.
>
> Have you never given any thought to the order of qualification inherent in the utilization of "of"?
>
> The resultant of any number multiplied by itself is the square of that number.
>
> ergo: miter length = root (two(thickness squared)) .
>
> Amazing what is lost as a result of the "whole language" system.

You should find another job other than trying to prove you are smarter
than everybody else. It's a crowded field. Besides, if you are going
to try to sound like Einstein, you should at least be right.

Charles Krug says...

> I hit Calc as a HS Senior in 1980, then again as a college freshman.
>
> MUCH later when I finished, I did Advanced Calculus (Sometimes called
> "Introductory Real Analysis" where you do all the proving.
>
> The other "prove it" courses were Discrete Mathematics (all about
> counting) and "Modern Algebra" (Properties of sets, operations, groups,
> rings, fields . . . )
>
> Great fun.

A math major? Mine was chemistry. I did differential and integral
calculus, analytic geometry and multivariate calculus with relative
ease. Then I got to linear algebra and differential equations and my
brain stopped working. It didn't help that we had a fresh PhD whiz kid
as the prof who hadn't learned how to dumb it down yet to us poor slobs
who were only minoring in math, not making it a career. Got a B in the
class, but it was only because everybody was flunking and he had to
resort to the curve to end all curves so that everybody didn't get an F.
My first semester calc instructor told us on day one there would be no
curve, even if it meant failing everybody. At the end, he said we were
the best calculus class he ever had and that four people had earned A's
(including me) and he hadn't given any A's at all in the previous three
semesters. The class was an hour long and he gave three hour tests--one
every two weeks and a take home test to go with the in-class test. We
took our final exam in the library because it was open until 10:00PM.
Our class time was at 6:00PM and he said he would be in the library at
4:30 if anyone wanted to start the test then. I arrived at 4:30 and
turned in my exam when the library was closing. Out of 25 story
problems, I still left three blank after 5 1/2 hours of work.

Duane Bozarth says...


> The notorious one for that when I was an undergrad was Atomic Physics
> lecture...each quiz was four problems, each counted 1/4-th, each was
> right or wrong--down to specific precision for those w/ numeric
> results. A real pita w/ a slide rule, for sure... :(
>
> Dr. Livesay, the ex-Marine drill sargeant was the ogre for Analytic
> Geometry (Calc IV) similar to your description...

The funny thing was our department chair was a Harvard man, and his were
the easiest advanced science classes I had.

Charles Krug says...

> My associates was in Engineering. When I got around to finishing
> *COUGHS* years later, I'd been working as a software engineer basically
> my whole career, so I signed up for CS, but the way the courses were
> laid out, doubling Math was "easy" to schedule (though a good bit more
> demanding than the CS classes).
>
> Linear is a stumbling block for CS types, much as (pick one) Statics and
> Dynamics or Differential Equations are for "hardware engineers."
>
> I found I had to study more than with some other courses, but it wasn't
> a brick wall. OTOH, fully a third of my section was either repeats
> who'd dropped or Math Ed grad students who didn't do well enough as
> Undergrads.

I could have done much better with the lin alg/Diff eq class if I had
applied myself the way I did with my first semester calc class, but I
just had so much more going on. I had Physical Chemistry (a lot of
abstract Max Planck quantum mechanics), very demanding labs, 300 level
general ed classes, seminars to attend and write reports on, undergrad
research, part-time job, etc. But I'll admit it was a great lifestyle
and I would be still doing it to this day If I could.

Prometheus says...

> I was 16 when I got to take calculus- and that was a year early, with
> a recommendation from the head of the math departement. There was no
> course higher than calc offered. Shame to say that in the three year
> gap between that and when I took calculus 2 in college, I forgot
> pretty much everything I had learned, and it really sort of soured my
> taste for higher maths.
>
> Horray for the American public education system!
>
>
> Aut inveniam viam aut faciam

I don't think Calc needs to be a high school class. If high schoolers
leave with a good knowledge of algebra, geometry and trigonometry they
will be very, very well prepared for college. When some graduates can't
find the USA on a globe, they have far bigger fish to fry.

> PDQ says...
>
> This is more fun that actually applying myself to wood.
>
> Have you never given any thought to the order of qualification
> inherent in the utilization of "of"?
>

Geometry is proveable. I took a course where we began with Peano's
postulates and from that derrived all of elementary Calculus--that stuff
with differentials and integrals you might have hit in college.

It took two semesters and was BRUTAL.

Lemme see if I remember . . .

There is a number Zero

(MANY things snipped)

. . . which proves that the limit exists about a point x0.

Easy peasy.

"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!

On Tue, 12 Apr 2005 22:30:29 -0500, Hax Planx <[email protected]> wrote:
> Charles Krug says...
>
>> I hit Calc as a HS Senior in 1980, then again as a college freshman.
>>
>> MUCH later when I finished, I did Advanced Calculus (Sometimes called
>> "Introductory Real Analysis" where you do all the proving.
>>
>> The other "prove it" courses were Discrete Mathematics (all about
>> counting) and "Modern Algebra" (Properties of sets, operations, groups,
>> rings, fields . . . )
>>
>> Great fun.
>
> A math major? Mine was chemistry. I did differential and integral
> calculus, analytic geometry and multivariate calculus with relative
> ease. Then I got to linear algebra and differential equations and my
> brain stopped working. I

My associates was in Engineering. When I got around to finishing
*COUGHS* years later, I'd been working as a software engineer basically
my whole career, so I signed up for CS, but the way the courses were
laid out, doubling Math was "easy" to schedule (though a good bit more
demanding than the CS classes).

Linear is a stumbling block for CS types, much as (pick one) Statics and
Dynamics or Differential Equations are for "hardware engineers."

I found I had to study more than with some other courses, but it wasn't
a brick wall. OTOH, fully a third of my section was either repeats
who'd dropped or Math Ed grad students who didn't do well enough as
Undergrads.

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"
>

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"
>

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" <[email protected]> wrote in message =
news:[email protected]...
| In article <[email protected]>, "PDQ" =
<[email protected]> 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?

This is more fun that actually applying myself to wood.

Have you never given any thought to the order of qualification inherent =
in the utilization of "of"?

The resultant of any number multiplied by itself is the square of that =
number.

ergo: miter length =3D root (two(thickness squared)) .

Amazing what is lost as a result of the "whole language" system.

--=20

PDQ
--
=20
"Robert Bonomi" <[email protected]> wrote in message =
news:[email protected]...
| In article <[email protected]>,
| PDQ <[email protected]> wrote:
| >Guess you never pretended to be logical.
| >
| >I said root(2(width*width)).
|=20
|=20
| Bzzzt! Thank you for playing.
|=20
| That may have been what you _intended_ to say (I'll not speculate on =
*that*),
| but it is *not* what you actually wrote.
| You wrote the English words for "root(2) * width*width"
|=20
| "root" is a 'higher priority' "operator" than 'times', and the =
associativity
| is left-to-right.
|=20
| Given that what you wrote above is what you actually intended to say
| originally, you omitted a critical phrase from your scrivening. The =
words
| "the quantity" was required after 'root of"
|=20
| >
| >My professors told me that, in the parlance, root equates to square
| >root. It is just a convenient form thereof.
|=20
| No argument on _that_ point.
|=20
| Did your professors bother to teach you about "reduction" to simplest =
form?
|=20
| Did your professors not teach you how *stupid* it is to do two =
multiplies
| and a (calculated) square-root when the exact same result can be =
obtained
| via a single multiply of a constant
|=20
| >Assuming you can comprehend the above, your underscore, via a caret, =
is
| >the same. I only wish I had a proper symbol on this pig.
|=20
| Tell me, just how would you express _in_words_, "root(2) * =
(width*width)"
| then?
|=20
| >"Robert Bonomi" <[email protected]> wrote in message
| >news:[email protected]...
| >| { *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]
| >|=20
| >| In article <[email protected]>,
| >| PDQ <[email protected]> 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.
| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| >| >
| >| >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.
| >|=20
| >| Actually, you *did*. And you even quoted those _exact_words_, =
above.
| >| "For clarity", the occurrences of the indicated words have been =
marked,
| >| so that the vision-impaired can locate them.
| >|=20
| >|=20
| >| >Better get your eyes checked. Your geekiness leaves much to be =
desired.
| >|=20
| >| "Speak for yourself, John" would seem to apply.
| >|=20
| >| >You might, however, be in line for the "Conehead" awards.
| >|=20
| >| You're the leading candidate for the pseudo-"Ronald McDonald" =
award.
| >| (The one named for the _original_ 'big red hair' circus =
entertainer, made
| >| Famous by Larry Harmon.)
| >|=20
|=20
|

In article <[email protected]>, "PDQ" <[email protected]> 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?

On Mon, 11 Apr 2005 10:50:59 -0700, David <[email protected]> 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

In article <[email protected]>, "PDQ" <[email protected]> wrote:
>"Hax Planx" <[email protected]> wrote in message =
>news:[email protected]...
>| PDQ says...
>|=20
>| > This is more fun that actually applying myself to wood.
>| >=20
>| > Have you never given any thought to the order of qualification =
>inherent in the utilization of "of"?
>| >=20
>| > The resultant of any number multiplied by itself is the square of =
>that number.
>| >=20
>| > ergo: miter length =3D root (two(thickness squared)) .
>| >=20
>| > Amazing what is lost as a result of the "whole language" system.
>|=20
>| You should find another job other than trying to prove you are smarter =
>
>| than everybody else. It's a crowded field. Besides, if you are going =
>
>| to try to sound like Einstein, you should at least be right.
>
>Can't say as I was/am trying to prove myself "smarter than the average =
>bear".
>
>I was just replying to a couple of pedants.
>
And you still don't realize where you went wrong.

--
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?

On Mon, 11 Apr 2005 10:27:33 -0700, David <[email protected]> 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%.

Sure wish you could add 1 + 1 with any consistency.

CIAO

--=20

PDQ
--
=20
"Doug Miller" <[email protected]> wrote in message =
news:[email protected]...
| In article <[email protected]>, "PDQ" =
<[email protected]> wrote:
| >=3D20
| >"Robert Bonomi" <[email protected]> wrote in message =3D
| >news:[email protected]...
| >| In article <[email protected]>,
| >| PDQ <[email protected]> wrote:
| >| >This is more fun that actually applying myself to wood.
| >| >
| >| >Have you never given any thought to the order of qualification =3D
| >inherent
| >| >in the utilization of "of"?
| >|=3D20
| >|=3D20
| >| Repeating (since you failed to address it last time):
| >| =3D20
| >| Tell me, just how would you express _in_words_, "root(2) * =3D
| >(width*width)"
| >| then?
| >| =3D20
| >Just for you: root two times width squared.
| >No "of", just processing.=3D20
| >1) do what's left of the "times"
| >2) do what's right of the "times"
| >3) multiply the two results together.
|=20
| Trouble is, that's *not* what "root two times width squared" means. =
Precedence=20
| of operators, remember? Exponentiation *and* root extraction (which is =

| simply exponentiation with a fractional exponent) are higher-priority=20
| operations than multiplication, and therefore "root two times width =
squared"=20
| means (the square root of two) times (the width squared).
|=20
| Seems you're having trouble grasping the concept, so let's try a =
simpler=20
| example: solve "four plus three times five".
|=20
| Do you get thirty-five, or nineteen?
|=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?

"Hax Planx" <[email protected]> wrote in message =
news:[email protected]...
| PDQ says...
|=20
| > This is more fun that actually applying myself to wood.
| >=20
| > Have you never given any thought to the order of qualification =
inherent in the utilization of "of"?
| >=20
| > The resultant of any number multiplied by itself is the square of =
that number.
| >=20
| > ergo: miter length =3D root (two(thickness squared)) .
| >=20
| > Amazing what is lost as a result of the "whole language" system.
|=20
| You should find another job other than trying to prove you are smarter =

| than everybody else. It's a crowded field. Besides, if you are going =

| to try to sound like Einstein, you should at least be right.

Can't say as I was/am trying to prove myself "smarter than the average =
bear".

I was just replying to a couple of pedants.


--=20

PDQ
--
=20

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" <[email protected]> wrote in message =
news:[email protected]...
| 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

>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

On Tue, 12 Apr 2005 19:54:21 GMT, Charles Krug
<[email protected]> wrote:

>Calculus--that stuff with differentials and integrals you might have hit in college.

College ? Don't you guys do this in secondary school?
(about age 13/14 ?)

In article <[email protected]>, "PDQ" <[email protected]> wrote:
>=20
>"Robert Bonomi" <[email protected]> wrote in message =
>news:[email protected]...
>| In article <[email protected]>,
>| PDQ <[email protected]> wrote:
>| >This is more fun that actually applying myself to wood.
>| >
>| >Have you never given any thought to the order of qualification =
>inherent
>| >in the utilization of "of"?
>|=20
>|=20
>| Repeating (since you failed to address it last time):
>| =20
>| Tell me, just how would you express _in_words_, "root(2) * =
>(width*width)"
>| then?
>| =20
>Just for you: root two times width squared.
>No "of", just processing.=20
>1) do what's left of the "times"
>2) do what's right of the "times"
>3) multiply the two results together.

Trouble is, that's *not* what "root two times width squared" means. Precedence
of operators, remember? Exponentiation *and* root extraction (which is
simply exponentiation with a fractional exponent) are higher-priority
operations than multiplication, and therefore "root two times width squared"
means (the square root of two) times (the width squared).

Seems you're having trouble grasping the concept, so let's try a simpler
example: solve "four plus three times five".

Do you get thirty-five, or nineteen?

--
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?

PDQ, to be consistent with your first post, you should use:
ergo: miter length = root (two(width squared))
OR
ergo: bevel length = root (two(thickness squared))

Sorry, given how the thread was going I couldn't help myself.

BadgerDog


"PDQ" <[email protected]> wrote in message
news:[email protected]...
This is more fun that actually applying myself to wood.

Have you never given any thought to the order of qualification inherent in
the utilization of "of"?

The resultant of any number multiplied by itself is the square of that
number.

ergo: miter length = root (two(thickness squared)) .

Amazing what is lost as a result of the "whole language" system.

--

PDQ
--

"Robert Bonomi" <[email protected]> wrote in message
news:[email protected]...
| In article <[email protected]>,
| PDQ <[email protected]> wrote:
| >Guess you never pretended to be logical.
| >
| >I said root(2(width*width)).
|
|
| Bzzzt! Thank you for playing.
|
| That may have been what you _intended_ to say (I'll not speculate on
*that*),
| but it is *not* what you actually wrote.
| You wrote the English words for "root(2) * width*width"
|
| "root" is a 'higher priority' "operator" than 'times', and the
associativity
| is left-to-right.
|
| Given that what you wrote above is what you actually intended to say
| originally, you omitted a critical phrase from your scrivening. The words
| "the quantity" was required after 'root of"
|
| >
| >My professors told me that, in the parlance, root equates to square
| >root. It is just a convenient form thereof.
|
| No argument on _that_ point.
|
| Did your professors bother to teach you about "reduction" to simplest
form?
|
| Did your professors not teach you how *stupid* it is to do two multiplies
| and a (calculated) square-root when the exact same result can be obtained
| via a single multiply of a constant
|
| >Assuming you can comprehend the above, your underscore, via a caret, is
| >the same. I only wish I had a proper symbol on this pig.
|
| Tell me, just how would you express _in_words_, "root(2) * (width*width)"
| then?
|
| >"Robert Bonomi" <[email protected]> wrote in message
| >news:[email protected]...
| >| { *VIEW IN A FIXED-PITCH FONT* e.g. 'fixedsys' on a Windows PC ]
| >|
| >| In article <[email protected]>,
| >| PDQ <[email protected]> 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.
| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| >| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| >| >
| >| >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 = 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.
| >| >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
| >| >| of the miter was proportional to "the square of the width of the
board".
| >| >
| >| >I don't think so. No where in the preceding, which I include herewith
| >| >for clarity, did I state what you saw.
| >|
| >| Actually, you *did*. And you even quoted those _exact_words_, above.
| >| "For clarity", the occurrences of the indicated words have been marked,
| >| so that the vision-impaired can locate them.
| >|
| >|
| >| >Better get your eyes checked. Your geekiness leaves much to be
desired.
| >|
| >| "Speak for yourself, John" would seem to apply.
| >|
| >| >You might, however, be in line for the "Conehead" awards.
| >|
| >| You're the leading candidate for the pseudo-"Ronald McDonald" award.
| >| (The one named for the _original_ 'big red hair' circus entertainer,
made
| >| Famous by Larry Harmon.)
| >|
|
|

In article <[email protected]>, "PDQ" <[email protected]> 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.
>
>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.

You *really* do have some reading comprehension problems. Go back and read it
again. Repeat until you realize your error.
>
>Better get your eyes checked. Your geekiness leaves much to be desired. =
> You might, however, be in line for the "Conehead" awards.

Nothing the matter with *my* eyes. Read it again, dolt.
>________________________________________________________
>--=20
>
>PDQ

--
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?

On Tue, 12 Apr 2005 22:13:00 GMT, Scott Lurndal <[email protected]>
wrote:
>>
>>>Calculus--that stuff with differentials and integrals you might have
>>>hit in college.
>>
>>College ? Don't you guys do this in secondary school?
>>(about age 13/14 ?)
>>
>
> Some do. Most don't. Modern schools no longer place any emphasis on
> learning - they are just socialization vehicles.
>

I hit Calc as a HS Senior in 1980, then again as a college freshman.

MUCH later when I finished, I did Advanced Calculus (Sometimes called
"Introductory Real Analysis" where you do all the proving.

The other "prove it" courses were Discrete Mathematics (all about
counting) and "Modern Algebra" (Properties of sets, operations, groups,
rings, fields . . . )

Great fun.

On Wed, 13 Apr 2005 07:09:18 -0500, Prometheus <[email protected]>
wrote:
> On Tue, 12 Apr 2005 22:51:22 +0100, Andy Dingley
><[email protected]> wrote:
>
>>On Tue, 12 Apr 2005 19:54:21 GMT, Charles Krug
>><[email protected]> wrote:
>>
>>>Calculus--that stuff with differentials and integrals you might have hit in college.
>>
>>College ? Don't you guys do this in secondary school?
>>(about age 13/14 ?)
>
> I was 16 when I got to take calculus- and that was a year early, with
> a recommendation from the head of the math departement. There was no
> course higher than calc offered. Shame to say that in the three year
> gap between that and when I took calculus 2 in college, I forgot
> pretty much everything I had learned, and it really sort of soured my
> taste for higher maths.
>

I had that problem. I (probably foolishly) tested out of Calc I and II
and dove directly into Calc III where I foundered.

Though I recovered. :)