![Photo of the header of our board of 'Drawing Hacks' - a piece of paper attached to a whiteboard which says 'Drawing Hacks - Try some out, or add your own!'](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215134140-1024x771.jpg)
At this year’s MathsJam UK Gathering, I had the pleasure of running one of the Saturday Night Tables – a chance to invite attendees at the Gathering to drop by and play with something. Together with fellow Manchester MathsJam regular Andrew Taylor, I ran a table of Mathematical Drawing Hacks – ways to make drawing complex mathematical objects and shapes easier.
I thought it’d be nice to share some of the ‘hacks’ we brought, and those others contributed – so I’ve included photos of each below, in case any of them are useful to you. Enjoy!
How to draw a Möbius Band
Andrew’s contribution (which slightly inspired the whole idea for the table). We all agree it’s a little bit ‘draw the rest of the owl‘, but I think it’s lovely.
![Diagram of drawing a Möbius strip by drawing a closed loop in the shape of a trefoil knot, then joining the edges](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215116581-808x1024.jpg)
How to draw a curly bracket ({)
This was my contribution – one of my students showed me this and it’s changed my life (intersection with the times when I have to draw a set bracket).
![Diagram showing that if you draw the letter S on top of a reversed letter S you get a {](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215120622-1024x723.jpg)
How to draw a tetrahedron in 3D
![Diagram of how to draw a tetrahedron by drawing a cube and joining two diagonally opposite top vertices and the opposite pair on the bottom](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215126062-741x1024.jpg)
How to draw an impossible triangle
![Diagram of how to draw an impossible triangle by starting with the centra triangle and extending the lines rotationally symmetrically, then adding more layers](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215106350-1024x552.jpg)
How to draw equally-spaced horizontals in one-point perspective
![Diagram of how to draw equally-spaced horizontals in one-point perspective, by constructing the third from lines going from the ends of the first through the midpoints of the second](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215101525-899x1024.jpg)
How to draw a mathematically plausible football (truncated icosahedron)
![Diagram of how to draw a mathematically plausible football (truncated icosahedron) starting from a pentagon, bisecting the exterior angles, turning those pieces into hexagons then filling in the rest](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215111535-1024x704.jpg)
How to draw a lower-case ash in one stroke
Thanks, Ash!
![Diagram of how to draw a lower-case ash (a symbol that's a lower-case A mashed into a lower-case E) in one stroke, starting in the top left and looping around](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215058167-966x1024.jpg)
Cool S
Scroggs just walked up and drew a Cool S and then left. Legend.
![A drawing of a cool S](https://aperiodical.com/wp-content/uploads/2023/11/PXL_20231111_215130658-751x1024.jpg)
Do you know of any cool drawing hacks you can share? Add them in the comments!
“I said consummate v’s! Consummate!”
Jeez!
To draw the expression for a rank-1 matrix in bra-ket notation, namely
\[
|v\rangle\!\langle w|
\]
Draw the first bar, then the v, then (this is the secret part) draw a capital-X, then finish the w and the bar.