question about terms

For those wishing to discuss the material found in The Art of Japanese Carpentry Drawing essay series.
ya
yanai

question about terms

Mon Jul 04, 2011 2:40 am

ok, i'm back with another question regarding wording. i have to admit that i've never really studied math and so i'm having problems at times with some of the wording. tired eyes may also have something to do with it.

volume I, page 42 of the essay (page 50 pdf) says that "the length opposite the angle under consideration" is labeled the "opposite." so is it correct then that the angle under consideration does not have to be an unknown angle? on page 42 it happens to be unknown.

on page 43 the known angle is 35゜and because we are considering this angle this determines the labeling of the lengths as opposite and adjacent?

i was confused and thinking that the "angle under consideration" meant the same as "the unknown angle" when in fact it simply means "the angle we are talking about (referencing) in each particular problem. is that correct?

thank you all...
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Yxoc
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Re: question about terms

Mon Jul 04, 2011 6:41 am

G'Day Yanai,
Firstly your endeavours to understand this material is commendable if you have no maths background - but once you understand some conventions and basic concepts, I believe it is accessible to anyone.

You are correct in that the angle under consideration may be known or unknown. That particular paragraph simply explains the convention - the two shorter sides in a right angle triangle are called the 'opposite' and the 'adjacent' but which is which is determined by the angle (always one of the less than 90 degrees angles) that you are referencing, and therefore the opposite and adjacent swap positions as you go from one angle to the other.

Hope this helps to clarify.

Regards

Derek
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Chris Hall
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Re: question about terms

Mon Jul 04, 2011 8:08 am

Well put Derek.
ya
yanai

Re: question about terms

Mon Jul 04, 2011 9:13 am

Yxoc wrote:G'Day Yanai,
Firstly your endeavours to understand this material is commendable if you have no maths background - but once you understand some conventions and basic concepts, I believe it is accessible to anyone.

You are correct in that the angle under consideration may be known or unknown. That particular paragraph simply explains the convention - the two shorter sides in a right angle triangle are called the 'opposite' and the 'adjacent' but which is which is determined by the angle (always one of the less than 90 degrees angles) that you are referencing, and therefore the opposite and adjacent swap positions as you go from one angle to the other.

Hope this helps to clarify.

Regards

Derek
thank you derek. i think i've got that then. i think it's a great sign that helpful explanations come from other members as well as from chris. it sets a great tone for the attitude of the study group.

cheers,
ya
yanai

Re: question about terms

Thu Jul 07, 2011 7:55 am

i finally am wrapping up TAJCD vol. I and i think most of it is beginning to sink in. i've been trying to set up formulas for the drawings before i move on to the explanations as a little test and for the most part they are right on.

for the final problem for vol. I i plugged numbers into another formula chris gave, which turned out to be a different one from those he used in the explanation to solve for the length of the footprint on the floor.

once we got the acute angle of 27.50228778 (27.50229 is the limit on my calculator at the moment), i plugged that into the formula "hypotenuse = 1/cos 27.50229" and got a unit length value for the hypotenuse of 1.127405. then because the width of the stick is 2" (double the unit value of radius 1), i multiplied that number by 2 and came up with 2.254811 (answer).

i thought that seemed to be the quickest way to the answer for me. are there any problems with that line of thinking? or can i count that as another tool in the toolbox?
ya
yanai

Re: question about terms

Thu Jul 07, 2011 8:07 am

the last problem for TAJCD vol. I has me thinking about something else.

the leg is splayed in two directions. that is the leg does not meet the beam at 90º in plan. does this second splay affect the cut angle of the leg in any way?, or is it mearly rotated 7" forward where it meets the floor from where it meets at the beam?

i'm not sure if i'm explaining myself very well.
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Chris Hall
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Re: question about terms

Thu Jul 07, 2011 8:56 pm

yanai wrote:i finally am wrapping up TAJCD vol. I and i think most of it is beginning to sink in. i've been trying to set up formulas for the drawings before i move on to the explanations as a little test and for the most part they are right on.

for the final problem for vol. I i plugged numbers into another formula chris gave, which turned out to be a different one from those he used in the explanation to solve for the length of the footprint on the floor.

once we got the acute angle of 27.50228778 (27.50229 is the limit on my calculator at the moment), i plugged that into the formula "hypotenuse = 1/cos 27.50229" and got a unit length value for the hypotenuse of 1.127405. then because the width of the stick is 2" (double the unit value of radius 1), i multiplied that number by 2 and came up with 2.254811 (answer).

i thought that seemed to be the quickest way to the answer for me. are there any problems with that line of thinking? or can i count that as another tool in the toolbox?

I think the way you went about solving that problem is perfectly valid Yanai-san.

That's the whole point - Pythagorean method and the basic trig functions are simply tools in the box. An awful lot can be done with your c2=a2+b2, but if you are comfortable with trig, sometime that is the fastest and most direct way to get to the answer. And if math is really not a good time, then developed drawing methods can solve most anything. They are all tools for getting to the results.

Good job, BTW!
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Chris Hall
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Re: question about terms

Thu Jul 07, 2011 9:01 pm

yanai wrote:the last problem for TAJCD vol. I has me thinking about something else.

the leg is splayed in two directions. that is the leg does not meet the beam at 90º in plan. does this second splay affect the cut angle of the leg in any way?, or is it merely rotated 7" forward where it meets the floor from where it meets at the beam?

I'm not sure if I'm explaining myself very well.
Yes, that leg is splayed, however it is also rotated, just like a typical hip rafter would be. By that I mean two of its sides are plumb. The cut on the foot is thereby beveled in only one direction. We will be dealing with that sort of sawhorse problem, but that will probably be 'sawhorse problem 2' or possibly '3' - first up will be the type where the leg is leaned in two directions, the arris of the stick (not the face) is plumb, and the cut on the foot is beveled on all faces.

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