———
on Thur, Apr 09, 2020, at 07:45 AM,la tagueuse élégante <catharine.cary@free.fr> wrote:
Dear Dadpop,
So I have this idea. I am imagining I have the run of a small theatre’s lobby for a year. By painting, papering, drawing and writing, gluing, designing, pasting, and adding on its walls, I imagine that after a year, after many shows and many patrons walking in and through, the theatre lobby will be one square meter smaller, its walls containing all the ideas, all over each other, wrapping from the interior, like the reverse of wrapping yarn around a ball. The ideas become architecture. If I were to do a design, it would look like this:
 |
My question: if the lobby were
10 square meters
15 square meters
or
20 square meters
for each of these scenarios, what would be
the thickness of my “tapestry” have to be,
to take away 1 square meter total?
Let’s assume the door is 60 cm. wide.
can you calculate that?
love and appreciation from,
your troublesome second daughter
|
———
On 10 Apr 2020, at 00:19, John W. Cary <divotness@fastmail.com> wrote:
The “lost area” figures you are requesting are a function of perimeter. The lost area is the product of perimeter and the thickness of your tapestry. Thus area alone is insufficient data.
For example, at 20 sq meters, if your room is 10×2 meters, the perimeter is 10+2+10+2 or
24 and the lost area 24 times the thickness of your tapestry. If the room was instead 40×1/2 meters, the perimeter is 40+40+1/2 +1/2=8 1and the lost area is 81 times the thickness of your tapestry. Obviously, the long skinny room would result in a thinner layer to make up 1 sq meter lost. I need width and length to do the calculations.
Dad
———
On Sat, April 11, 2020 at 11:19 AM, la tagueuse élégante <catharine.cary@free.fr> wrote:
hi again,
the estimated width of the room is 3 meters and the length 5 meters, can
you figure it out now? Right nOW!!!! before you get on your plane? My proposal is due on Thursday! thank you so very much,
xx
———
On Sat, April 12, 2020 at 00:19 AM, John W. Cary <divotness@fastmail.com> wrote:
If the room you have in the theatre lobby is 3 x 15 meters, the total area is 3×5=15m2.The net length of the tapestry is 2x(3+5-2t)= (16 – 4t) m, where t is thickness of the the tapestry and reduction is made for corner overlap.
The lost area (you want 1 sqm) is the net length x t = (16-4t)t or 16t-4 t squared.
At lost area equal to 1 sqm, 16t-4tsq = 1. Simplifying to 16t-4tsq-1=0. Dividing by 16 yields t-1/4tsq-1/16=0.
Assuming t is small, we can discount 1/4t(sq) as “too small to matter,” then this reduces to t-1/16=0 or t = 1/16 m or .0625m or 6.25cm at 2.54cm/in, that works out in the American system to about 2 1/2
inches. as a check, our estimate of net length is 16t so the lost area should be 16 x . 0625 which equals exactly 1 sq m.
This may be correct.
Dad
Democracy Wall? 14 Street Union Square subway December 2, 2016. Photo: Peter Eckersall