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Mathematical Drawing Hacks

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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!'

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

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 {

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

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

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

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

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

Cool S

Scroggs just walked up and drew a Cool S and then left. Legend.

A drawing of a cool S

Do you know of any cool drawing hacks you can share? Add them in the comments!

3 Responses to “Mathematical Drawing Hacks”

  2. Avatar Ryan O

    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.

    Reply

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