solution on a torus
the torus is represented by the rectangle, with its top and bottom edges identified, and its left and right vertical edges identified
(if it helps, picture first pushing top and bottom away from you while rolling into a horizontal tube, with those edges meeting and sealing at the back. then make the tube long and flexible, and curve with the midsection coking towards you and the circular ends of the tube pushed back from you on a curve, forming the doughnut shape when the circular openings meet at the back and seal)
Just a day after reading https://arnoldzwicky.org/2021/03/29/pruners/ about these tools, I ran across this clip.
Season 2 episode 3 “No connection”
Paul (Martin Freeman)
Jim (Paul’s father) (Alun Armstrong)
Jackie (Paul’s mother) (Joanna Bacon)
from 12:06 to 12:30
Paul: Hey. You all right, Mum?
Jackie: I’ve been doing Lynn’s roses for years. Since she got arthritis in her hands, and couldn’t work the — oh, what are they called, Jim?
Jackie: Secateurs. … so, I’d nip in and do some deadheading or pruning.