iiinova — where your digital self keeps evolving

Andrew Stacey @mathforge.org · 24/09/2026

Anyone making a slasher movie on the cheap and want a prop? Forgot to empty my pockets when putting my school clothes in the washer. #ITeachMaths

A towel with mysterious red marks on it, that could be blood but are more likely to be from the red pen I accidentally put in the washing machine.

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Andrew Stacey @mathforge.org · 14/09/2026

Folding some origami cranes, I got curious as to whether they could be made to interlock to make a modular origami model. It's not a great lock, but it shows it works in principle: the head and tail of the crane are flattened and tuck into the wings of its neighbours. #origami #mathsky

A modular origami model, where the model is based on the crane. The beak and tail interlock with the wings of its neighbours. Tgis model has six modules, so exhibits cubical symmetry.

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Andrew Stacey @mathforge.org · 27/08/2026

Remember folks, when on holiday do *not* feed the local wildlife. They might try to follow you home.

The Headington shark. That is, a large fibreglass model of a shark sticking out of the roof of a terrace house in Headington (a suburb of Oxford).

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Andrew Stacey @mathforge.org · 27/08/2026

Normally, I'm against the practice of sending a small item in a large box, but I the case of Hagoromo chalk, I'll make an exception. The amount of packaging required to deliver it unharmed feels totally acceptable. #mathsky

A box of hagoromo chalk in front of the frankly insane amount t of packaging that was required to post the chalk unharmed.

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Andrew Stacey @mathforge.org · 06/08/2026

Well, I had to ask, didn't I? Pros: it's smooth, without being overly analytic. Although individual support is guarded [bounded], taken together, it's total. Cons: can be a bit derivative, and while many norms are accepted, they rapidly decrease after a bit. Felt a bit dark [Schwartz]. #mathsky

A poster on the side of an old-fashioned English pub saying "Ask us sbout our function space"

Below that, it says "Available for all occasions" and then "Please speak to a member of the team for more info"

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Andrew Stacey @mathforge.org · 14/07/2026

Proof that the vikings got as far as Japan.

A label on a pack of origami paper from Hobbycraft. The label reads "Creativity the Scandinavian way".

The rest of the label contains samples of the paper: all are greyscale with patterns on both sides, most patterns are based on a simple geometric design with one more floral and one based on handwriting.

The pack contains 50 assorted sheets, 80g, and 10×10cm.

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Andrew Stacey @mathforge.org · 02/06/2026

Raising a glass to Richmal Crompton and Matryn Jarvis. (No reason, other than the drink reminded me of listening to him reading her stories)

A glass of what might be mistaken to be whiskey, but is actually a cold brew liquorice tea - which might be called "liquorice water", much beloved by William Brown of the Just William stories.

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Andrew Stacey @mathforge.org · 02/06/2026

Wanted to see how much @chadtopaz.bsky.social 's new book costs. Intrigued by the prospect of a sale from the publishers. Not too sure the discount is really offering much, here. #CoreMaths

A screenshot from the Princeton University Press website advertising a discount. Only the actual amount is obscured by a weird icon so it reads "0% off most titles, May 4 to June 9"

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Andrew Stacey @mathforge.org · 26/05/2026

Magic roundabouts seem to be appearing everywhere these days. I drove round this one in Hemel Hempstead earlier today. The red lines of traffic are simply people trying to figure out which way round it to drive.

Screenshot of google maps showing a "magic roundabout" in Hemel Hempstead with six mini roundabouts. The traffic colours are showing most routes in red.

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Andrew Stacey @mathforge.org · 03/05/2026

'Yet a sensitive heart the rhinoceros owns, If you doubt it here's the proof: That thing on his nose is for getting stones Out of a horse's hoof. He seldom - if ever - meets a horse (It is this that makes him sad) When he does then it hasn't a stone in its hoof But he would if he did and it had!

A baby rhinoceros next to an adult rhino, both facing towards the camera.

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Andrew Stacey @mathforge.org · 03/05/2026

'Oh, nobody likes the rhinoceros much If you ask the reason why They will say because of his scaly touch Or his hard, unflattering eye. But should you ask a truthful man You will get this quick response: "I do not trust that thing on his nose - The bodger on his bonce!" #Cotswolds

Two rhinoceroses (rhonoceri?) at Cotswolds Wildlife Park, facing each other with the shape of their heads and horns making a lovely parabola.

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Andrew Stacey @mathforge.org · 25/02/2026

Now *that's* not confusing at all! @vmnalex.bsky.social (Admittedly, both notations are correct, but it's a clear example of the point that notationis insufficient) #UKMathsChat #ALevelMaths

An except from the UK government a level maths specification showing the notation for ordered pairs, (x,y), and for open intervals, (a,b).

Between them are notations for closed and half-open intervals.

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Andrew Stacey @mathforge.org · 09/02/2026

Had a go at the great-granny knot in TikZ, @cubesart.bsky.social

A great-granny knot, consisting of a trefoil where each outer lobe is again a trefoil.

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Andrew Stacey @mathforge.org · 06/02/2026

Made a stab at explaining intersecting planes in Y12 Further Maths, wasn't sure it was all that clear, then turned round to see that my students had made their own version. #MathsToday

Three pieces of paper, interlocking to illustrate three intersecting planes. The pieces of paper were cut so that they could pass through each other.

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Andrew Stacey @mathforge.org · 24/01/2026

But the trolls in Norway are so friendly now, and hardly ever eat people. Even if they got trip-trapity over their rickety-rackety bridge.

A tree in a Norwegian forest with a face painted on it consisting of two eyes and a smiley mouth.

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Andrew Stacey @mathforge.org · 20/01/2026

Trying to figure out which LaTeX package this is from.

Graffiti on a fence in Oxford which reads "Nice One" in large letters. What makes it notable is that the graffiti artist has taken the time to add serifs and other font niceties.

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Andrew Stacey @mathforge.org · 21/12/2025

Buying hot dogs today. The prices per 100g on the signs are a bit blurred, they were 27.7p per 100g for the jar of 12 and 43.4p per 100g for the jar of 6. After staring at them for some time, and using a calculator to double check, I did buy the jar of 12 as it was the cheaper option. #UKMathsChat

A photo of different sizes of jars of hot dogs, from the Iceland supermarket in the UK.

The jar with 12 hot dogs costs £2.85 and the label says it is 27.7p per 100g.
The jar with 6 hot dogs costs £1.50 and the label says it is 43.5p per 100g.

Also relevant are the weights. The jar of 12 weighs 1030g net, and 720g drained. The jar of 6 is 345g net and 180g drained.

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Andrew Stacey @mathforge.org · 14/12/2025

Waterstones in Oxford has recently moved across town (nearer the Westgate, further from Blackwell's - which they now own). Some things didn't change in the move. They still stock Good Books. Strong recommend for Christmas.

A book display in Waterstones bookstore in Oxford showing science books including "The Mathematician's Library" by Tom Briggs

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Andrew Stacey @mathforge.org · 18/11/2025

Here you go!

$A circular braid on six strands, rendered with yellow strand colour on a black background. The braid word is: a_3^{-1} a_2^{-1} a_4 a_2 a_4 a_3 a_1 a_1^{-1} a_3^{-1} a_5^{-1} a_3 a_2^{-1}$

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Andrew Stacey @mathforge.org · 26/10/2025

I even found a copy in that intellectual backwater that is Cambridge . @teakayb.mathstodon.xyz.ap.brid.gy

A display in Heffers bookstore in Cambridge with "the mathematician's library" in amongst other popular science books.

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Andrew Stacey @mathforge.org · 22/10/2025

They say that if you stay long enough in the Norrington Room then every author in the country will come and sign your book. Spotted in Oxford's unique bookshop - @teakayb.mathsy.space

A photo of books lying on a shelf in the Norrington Room in Blackwell's bookshop in Oxford. Visible is "The Mathematician's Library" with two other bookish books.

A photo of books on display in the Norrington Room in Blackwell's bookshop in Oxford. Visible is "The Mathematician's Library" in the centre of the display with many other books around it.

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Andrew Stacey @mathforge.org · 26/08/2025

Feels more like a channel 4 program than bbc, but good to see that the water companies are trying different things to clean up their pipes.

A headline from the BBC website, advertising a program on iplayer, that reads "Which aspiring sewer will measure up to impress the judges?"

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Andrew Stacey @mathforge.org · 21/08/2025

"What the tumbledryer hath bound together, let not man put apart."

Cords from clothing that have been twisted and intertwined after being in the tumbledryer.

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Andrew Stacey @mathforge.org · 05/08/2025

I have a query about one of @catrionaagg.bsky.social 's puzzles. The goal is the area of the red quarter circle. I have a solution that *doesn't* use the semi-circle. Am I missing something, or is that semi-circle irrelevant? #geometrypuzzles notes.mathforge.org/notes/publis...

A right angled triangle with a filled red quarter circle with centre at the right angle and which is tangential to the hypotenuse. The hypotenuse is divided into three equal parts, each labelled "2". The point of tangency of the quarter circle is at a division point, with one part above and two parts below.

Also in the diagram is a semi-circle which has centre on one of the non-hypotenuse sides and which meets tangentially the hypotenuse at the other division point.

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Andrew Stacey @mathforge.org · 04/08/2025

For some reason, linking directly to an image doesn't fetch a preview of that image. That's annoying. Anyway, here's the image for that puzzle. #mathsky #geometrypuzzles

One of Catriona Agg's puzzles. It consists of four equal-sized squares aligned horizontally with four equilateral triangles on top - one triangle per square - and of the same side length as the squares. These are contained within a semi-circle so that the squares sit on the base of the semi-circle and the arc just touches the tops of the outer two equilateral triangles. The diameter of the semi-circle has length 4.

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Andrew Stacey @mathforge.org · 28/07/2025

To which I'll add another bat, this one made from quadratics. loopspace.mathforge.org/CountingOnMy...

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Andrew Stacey @mathforge.org · 25/07/2025

There's also code.mathforge.org/axes/ It puts the numbers at the lines, not in the gaps, and the axes labels are at the ends, not the middles. I should also make it so that you can hyperlink to a set of configurations ...

Axes with horizontal from 0 to 24, labelled "Days", and vertical from 0 to 6, labelled "Workers".

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Andrew Stacey @mathforge.org · 13/07/2025

This took the combined mental effort of two Oxford graduates and one Cambridge undergraduate to figure out how to remove the base from the rest of the pen. It's designed to be filled with water for painting with watercolours. #mathsky #UKMathsChat #ITeachMaths

A water-fillable pen (for painting with watercolours). The body of the pen can be removed to fill with water.

However, it is reverse-threaded. Something that took us a long time to spot.

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Andrew Stacey @mathforge.org · 10/07/2025

$Rendering of "3<=4" where the less-than-or-equal sign has a slanted extra line instead of the more common horizontal one. As a bonus for reading the alt-text, the LaTeX command for this is \leqslant.$

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Andrew Stacey @mathforge.org · 01/07/2025

Anyone know what entity ͏ is? The BBC seems quite keen on it.

An email heading with the subject "Last chance to give your opinion on the BBC" and snippet that reads "BBC - BBC" followed by two lines consisting of just repetitions of "͏"

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Andrew Stacey @mathforge.org · 22/06/2025

Very useful list! Turns out I already have one of your recommendations...

A booklet entitled "How do undergraduates do mathematics?" by Charles Batty, dated April 1994

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Andrew Stacey @mathforge.org · 21/06/2025

If you need a good number puzzle you can always rely on @emmaemma53.bsky.social to set a sneaky one!

$A presentation slide with the title "Challenge!" below which is the calculation: 2/3 ÷ 4/9 × 5/6 ÷ 3/4 × 3/5 Below that is written: "Can you write your own question using a string of multiplication and divisions of fractions, which gives the same result?"$

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Andrew Stacey @mathforge.org · 12/06/2025

This generated the right question! And an excellent discussion ensued. #MathsToday #UKMathsChat

A rectangle drawn on squared paper of 3 by 5 squares with the question "how big is this rectangle?" written inside it.

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Andrew Stacey @mathforge.org · 25/05/2025

"Where's the Norwegian dictionary?" "The what?" "Norwegian dictionary - you know, den blå ordboka" "Blue? What shade of blue?" "Dark, I think." "Then it should be top left." #HalfTermMadness #MySOMadeMeDoIt #ActuallyQuiteFun

Three bookshelves (Billy bookcases from Ikea, in case you were wondering) with the books sorted by colour. Blue on the left, green and black in the middle, and red fading to white on the right.

The image is blurred in case anyone's a bit judgemental about my choice of reading matter

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Andrew Stacey @mathforge.org · 28/04/2025

What seems to be forgotten in all the recent kerfuffle about maths in sport is that the Fibonacci sequence *does* have a very close relationship with football! With *the* football itself, that is. Assuming it is correctly drawn, that is. #UKMathsChat #ITeachMaths

A spiral of isosceles triangles based on the Fibonacci sequence. Each triangle's sides are successive pairs of numbers from the sequence, with the smaller number repeated. Then the triangles are aligned with their edges of common length to form a spiral.

The ratio of the sides approaches the golden ratio, and an isosceles triangle with sides in the golden ratio forms part of a regular pentagon.

Therefore, by taking one of these isosceles triangles a close approximation of a regular pentagon can be drawn.

The diagram also shows circles used to construct the triangles, and the final triangle (corresponding to Fibonacci numbers 13 and 21) is extended to an almost regular pentagon. The pentagon is filled in translucent red, appropriate to the football team that completed the sequence.

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Andrew Stacey @mathforge.org · 22/04/2025

Gave my Y9s this diagram for #MathsToday. Picked a few numbers for a,b,c and then their task was to work out all the lengths and angles. Next lesson we'll cut it out and reassemble it and they'll discover that they've secretly been doing 3D trig! #UKMathsChat #ITeachMaths

A partial net of a cuboid box together with certain triangles that fill in various diagonals. Specifically, the base and two adjacent sides of the box, then a triangle that lies over the base to give the diagonal of the base, this joins to two triangles that (when assembled) would be vertical with one giving the diagonal of a side and the other the diagonal across the whole box. Finally another triangle to join these last two diagonals together.

Various lengths that become sides of the cuboid are labelled a,b,c so that all lengths can be determined in terms of these three lengths.

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Andrew Stacey @mathforge.org · 11/04/2025

Visited the "Listen on the Rafio" exhibition at the Weston library, courtesy of @bodleianlibraries.bsky.social . Very stuck by this cartoon from shortly after the newfangled wireless was available. What's that saying? Plus ça change, plus c'est le meme chose.

A cartoon from the 1920s (or soon after) decrying how social interaction has changed since the introduction of the "wireless". It depicts two dinner scenes, in one everyone is engaged in conversation, in the other then everyone sits staring into space with headphones on.

The first scene has the caption "the dinner-parties of our ancestors were embellished with sparkling conversation". The second "Byt nowadays the talking is done "off"."

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Andrew Stacey @mathforge.org · 10/04/2025

Latest modular origami. 90 sonobe modules connected internally, colouring scheme has 6 colours, all vertices have distinct colours, scheme relates to the dodecahedral symmetry. Base is five cubes linked as the model isn't quite as rigid as I'd like for it to rest on one of its faces. #origami

A 90 module modular origami model, with 6 colours: dark blue, sea blue, pale green, yellow, red, and purple. No edge meets another of the same colour. The modules are joined inside the model so that each edges carries just its own colour.

The model rests on a base which is made from five connected cubes in black paper.

The model is sat on a wooden surface, with a purple crocus in a small vase behind it and the edge of a mantlepiece clock just visible alongside.

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Andrew Stacey @mathforge.org · 22/03/2025

Feels a tad harsh, but perhaps a fair description of generative AI.

A notification that says: Recommended for you. We thought you'd like a robotic vacuum.

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Andrew Stacey @mathforge.org · 17/03/2025

Let's see if I can upload a video ...

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Andrew Stacey @mathforge.org · 04/03/2025

Here's a different version. In this, I've taken a chunk out of the blue rectangle equal to the red rectangle. With this design then the blue shape tessellates perfectly with the parallelogram tessellation.

A figure containing three separate diagrams, all based on a parallelogram decorated with rectangles. Let the parallelogram have vertices at (0,0), (a,b), (c,d), and (a+c,b+d). Then there is a blue rectangle with corners at (0,0), (a,0), (0,d), and (a,d). In the first diagram, there is a red rectangle of width c and height d located in the corner of the blue at the (0,d) vertex.

In the second diagram, the red rectangle is excised from the blue rectangle to leave an L-shape.

In the third diagram then the second diagram is repeated with the parallelogram tessellating. The blue L-shapes also tessellate, showing that the parallelogram and blue shape have the same area.

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Andrew Stacey @mathforge.org · 03/03/2025

Today's prompt is "nature". I don't subscribe to the view that nature has *any* occurences of either the golden ratio or Fibonacci sequences. But sunflowers are nice. #MathArtMarch

A sunflower spiralling in to its centre, so that the petals of one turn overlay the seeds of the previous.

$A pattern based on tangential circles with a central large circle and then decaying away symmetrically to the sides, with smaller circles filling in the gaps between the main circles and the x-axis to create a fractal pattern. Then in place of the circles, sunflowers are drawn.$

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Andrew Stacey @mathforge.org · 02/03/2025

Thinking about the fact that the link between determinants and area is on the spec so, despite my misgivings, I have to cover it. So here's an approach I don't fully loathe ... Area of parallelogram is area of blue rectangle minus area of red. Proof: tessellation. #ALevelMaths #mathsky

The figure consists of a core diagram and then a tessellation in which that core diagram forms the repeated pattern.

The core diagram consists of two rectangles and a parallelogram. The rectangles are blue and red. The rectangles share a vertex, and at that vertex then the sides of the rectangles form two straight lines. The parallelogram has two opposite vertices located each at the vertex of a rectangle opposite to the one where the rectangles meet. The other two vertices of the parallelogram are on the sides of the blue rectangle adjacent to where it meets the red.

The tessellation pattern uses the parallelogram as its tile. The rectangles are drawn on top, and the blue rectangles of each tile overlap with those of its neighbours in such a way that the overlap is exactly the red rectangle.

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Andrew Stacey @mathforge.org · 02/03/2025

On a square grid. We'll, you don't get much square-er than a spreadsheet! Source: loopspace.mathforge.org/HowDidIDoTha... #MathArtMarch

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