Andrew Stacey
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mathforge.org
Andrew Stacey
@mathforge.org
1.6K followers 440 following 2.4K posts
Mathematician: formerly academic (differential topology), currently educational (Head of Department in a UK secondary school).

Side interests in Maths & Programming & Art.

Website: https://loopspace.mathforge.org
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mathforge.org
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}
November 18, 2025 at 8:18 PM
mathforge.org
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.
October 26, 2025 at 8:33 PM
mathforge.org
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.
October 22, 2025 at 5:52 PM
mathforge.org
Oh dear!

#ALevelMaths #UKMathsChat #ITeachMaths #mathsky
Text from an a level textbook defining the Maclaurin series of a function f(x) and saying that the series is valid provided that all derivatives have finite values at 0. The claim is that this converges to f(x).
October 14, 2025 at 10:21 PM
mathforge.org
#TikZfun
A blue path and a red path, both sine waves and slightly offset horizontally. The paths a split so that the appear to twist around each other. They are rendered with a pen effect so that the line thickness varies as if drawn with a calligraphic pen.
October 1, 2025 at 8:59 PM
mathforge.org
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?"
August 26, 2025 at 8:13 PM
mathforge.org
"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.
August 21, 2025 at 6:23 PM
mathforge.org
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.
August 5, 2025 at 5:48 PM
mathforge.org
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.
August 4, 2025 at 6:38 PM
mathforge.org
To which I'll add another bat, this one made from quadratics.

loopspace.mathforge.org/CountingOnMy...
A version of the batman logo drawn with quadratics and straight lines. The quadratics and lines are drawn in yellow, with the logo itself filled in black.
July 28, 2025 at 2:13 PM
mathforge.org
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".
July 25, 2025 at 3:33 PM
mathforge.org
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.
July 13, 2025 at 7:15 PM
mathforge.org
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.
July 10, 2025 at 10:32 PM
mathforge.org
Anyone know what entity &#847; 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 "&#847;"
July 1, 2025 at 8:13 PM
mathforge.org
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
June 22, 2025 at 2:40 PM
mathforge.org
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?"
June 21, 2025 at 5:02 PM
mathforge.org
Look, Ma! No small angle or compound angle!

#ALevelMaths #MathsToday #UKMathsChat
The title is "Radians" A unit circle with a radius drawn at angle θ to the horizontal. The coordinates at that point are marked (cos (θ), sin (θ) ). A tangent line is drawn and labelled with the vector with components -sin(θ) and cos(θ) to indicate the tangent vector of unit length. A stick figure is drawn at the marked point and the diagram has the legend: "Walk around the circle at speed 1 unit per second, it would take 2π seconds to go round." Off to the far side of the diagram is a second stick figure with a label "only sees the vertical motion" and then is written: podition: sin(θ) velocity: cos(θ) The caption to the whole figure is: "Radians is time taken to get to that angle"
June 12, 2025 at 9:14 PM
mathforge.org
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.
June 12, 2025 at 8:27 PM
mathforge.org
"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
May 25, 2025 at 4:56 PM
mathforge.org
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.
April 28, 2025 at 7:25 PM
mathforge.org
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.
April 22, 2025 at 8:09 PM
mathforge.org
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"."
April 11, 2025 at 9:30 PM
mathforge.org
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.
April 10, 2025 at 2:52 PM
mathforge.org
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.
March 22, 2025 at 3:45 PM
mathforge.org
Let's see if I can upload a video ...
March 17, 2025 at 10:10 PM