Forgot my geometry...

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| >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? | Just for you: root two times width squared. No "of", just processing. 1) do what's left of the "times" 2) do what's right of the "times" 3) multiply the two results together.
--
PDQ --
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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?
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Sure wish you could add 1 + 1 with any consistency.
CIAO
--
PDQ --
| >| >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?
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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?
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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?
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wrote:

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
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You gotta go that deep to see how much your IRS refund is.
Other than then, who cares for more than a silly millimeter?
--
PDQ --
| >>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 | |
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something ......and in reply I say!:

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))"
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David wrote:

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

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Thanks all. I'm about to make the cuts now. 'preciate the help.
Dave
David wrote:

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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%.
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"D" == "claimed thusly:
D> I've got a board set at a 45 degree angle, back from a line. How much D> (percentage) of the length of the board does it take up? To D> conceptualize the issue, I drew a one inch line on paper with a ruler, D> and rotated the ruler to a 45 degree angle, thinking that the one inch D> mark on the ruler would be only 1/2 away from the starting point (along D> the original path of the ruler), but it looks like it's about 90% along 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) = opposite / hypotenuse cos (angle) = adjacent / hypotenuse tangent (angle) = 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 = 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) --
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; I for Amiga, the world IBM clones.
Esksznk, Esksznk, hogy rabok tovbb nem lesznk!
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