Craftsmanship in Wood

One of the members is having a problem posting and keeps getting an error message, which I'm trying to resolve. in the meantime, on behalf of Craigak, i'll post his question:

"

OK. So here is my question to be posted in TAJCD Vol.II:
on p. 87 you state:
Compare the triangle we started with, A~B~C, to the one we finished with, A'~B'~C'.
It is apparent immediately that they share the same measure of horizontal displacement, kō (勾) however the vertical displacement of A~B (殳) of the original triangle has effectively
stretched to become the measure A'~B' (玄).
I am not getting this...the stretched part. And why is this now labeled 'gen'?
My forehead is not yet burning and I will continue to study!

"

Would anyone like to tackle that one?

G'Day Craigak - hope your write permissions are sorted shortly, and welcome to the forum. Let me try and help your understanding of the problem at hand. As a precursor let me say that simply reading the material through several times is the antidote to many problems, I found that it took a little time, and several readings at times, to visualise in 3D what the 2D drawings represented.


Firstly I think you have misunderstood the material on a small point. The Ko (A'-B') length of the new triangle A'-B'-C' is not relabeled as Gen but is the same length as the Gen of the original triangle A-B-C, so the material simply makes the point that the Gen of the original triangle and the Ko of the new triangle are the same length. Otherwise Gen simply means hypotenuse so the new triangle has it's own Gen - side A'-C'.

Stretching - When Chris explains that the Ko of the new triangle has been stretched he is partly speaking figuratively, but in a way it is true because the triangle A-B-C, in being projected onto the sloping board of our hopper, does become stretched in the vertical dimension. Imagine your old school projector and you project an image of the rise/run triangle (A-B-C) onto the screen, orientated in exactly the same way as in the diagram on page 87. BUT... someone has taken the screen and sloped it towards you so that the top edge of the screen is closer to you than the bottom edge. The image on the screen will be lengthened in the vertical plane and the greater the slope the greater the distortion. You could go up to the projected image and measure the three sides of the triangle and find that the short side length is unchanged (because the screen is square to you from left to right) but the Ko is longer (because it slopes towards you from bottom to top).

Hope this helps your understanding, but happy to reattack it if you're still in the wilderness.

Regards

Derek

Derek,
A projector: that's a brilliant analogy - I can use that.
Rob

Derek,

that was a good analogy - perhaps you would allow me to use it in the essay in a future revision? I'm thinking that Craig may not be the only person having struggle with that concept.

~Chris

Hi to all,
Derek, that is a great way to explain it . Thank you!
Back to reading on this staggeringly hot Sunday in Chicago.

Craig

Well look who's up and posting! Good to see.

Thanks Guys - analogies are my speciality .

Chris - more than welcome to use the idea in any of your writings.

As I read my comments now they sound a little presumptuous:

"When Chris ... he is partly speaking figuratively"

I can't talk on any one else's behalf, and I cannot divine anyone's exact intent when writing. It should read something like:

"I believe Chris is speaking figuratively" or "I don't believe the material is being literal"

Regards

Derek