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"
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:
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 5.65685424949238019520675489683879It 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
| (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
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.
Try again. Square root of 2 times the width of the board _not_ squared.
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.
Yes. Proportional to the width. Not to the square of the width.
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?
Thanks all. I'm about to make the cuts now. 'preciate the help.
Dave
David 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.
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
| >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?
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 5.65685424949238019520675489683879It 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
| (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
| >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?
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%.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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.
"Speak for yourself, John" would seem to apply.
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.)
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
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
| >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.) |
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
| >>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 |
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"
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
Tell me, just how would you express _in_words_, "root(2) * (width*width)" then?
You *really* do have some reading comprehension problems. Go back and read it again. Repeat until you realize your error.
Nothing the matter with *my* eyes. Read it again, dolt.
-- 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?
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
| >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 | >| >| >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 |
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 ]
Yes, everybody understands that. Too bad you slept through the class where they discussed precedence of operators.
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?
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
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.
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