Andrew Stacey

@mathforge.org

1744 Followers 452 Following

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

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.
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.
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"
Screenshot of google maps showing a "magic roundabout" in Hemel Hempstead with six mini roundabouts. The traffic colours are showing most routes in red.
A baby rhinoceros next to an adult rhino, both facing towards the camera.
Two rhinoceroses (rhonoceri?) at Cotswolds Wildlife Park, facing each other with the shape of their heads and horns making a lovely parabola.
An arrangement of seven squares. Six of the squares are identical and are arranged so that reading from left to right they form three stacks that abut and are of heights 2,3,1, with each base square aligned with the second square in the stack to its left. A tilted larger square overlays the six and shares a vertex with the lower right vertex of the bottom-most square. The top left vertex of the uppermost of the six squares lies on an edge of the larger square. A line is drawn from the left-hand vertex of the larger square to the lower right vertex of the rightmost small square. The angle formed by this line and the left-hand edge of the larger square is marked with a question mark.
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.
A great-granny knot, consisting of a trefoil where each outer lobe is again a trefoil.
Three pieces of paper, interlocking to illustrate three intersecting planes. The pieces of paper were cut so that they could pass through each other.
A tree in a Norwegian forest with a face painted on it consisting of two eyes and a smiley mouth.
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.
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.
A book display in Waterstones bookstore in Oxford showing science books including "The Mathematician's Library" by Tom Briggs
Three squares side by side with a fourth that shares a corner with the right-hand most and passes through the corners shared by the left and middle. The extremes of the tilted and left squares are joined, to form an angle.
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}
A display in Heffers bookstore in Cambridge with "the mathematician's library" in amongst other popular science books.
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.
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).
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.
A headline from the BBC website, advertising a program on iplayer, that reads "Which aspiring sewer will measure up to impress the judges?"
Cords from clothing that have been twisted and intertwined after being in the tumbledryer.
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.
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.
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.
Axes with horizontal from 0 to 24, labelled "Days", and vertical from 0 to 6, labelled "Workers".
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.
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.
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;"
A booklet entitled "How do undergraduates do mathematics?" by Charles Batty, dated April 1994
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?"
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"
A rectangle drawn on squared paper of 3 by 5 squares with the question "how big is this rectangle?" written inside it.
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
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.
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.
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"."
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.
A notification that says: Recommended for you. We thought you'd like a robotic vacuum.
A video showing how to make a right-angled triangle. At the start there are three lengths labelled 4, 8, 16. Copies of the three lengths then move to the centre of the screen. The short length moves to overlap the long length (coinciding at the left hand end), which then folds. The fold point is so that the right hand end of the long length is folded to touch the right-hand end of the short length. With the lengths chosen, the fold point is at (16 + 4)/2 = 10 from the left-hand end. The long length then unfolds until the distance between its ends is the same as the middle length, which then moves to connect these ends forming a triangle. Because of the lengths initially chosen, the triangle is a right-angled triangle.
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.
A sunflower spiralling in to its centre, so that the petals of one turn overlay the seeds of the previous.
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.
A Julia set displayed on a spreadsheet.
A gothic font from the lettraset catalogue (old english) showing a J slightly descending below the baseline.
Screenshot of my reputation bar on the website https://tex.stackexchange.com . My reputation is 157,314 (then I also have 46 gold badges, 400 silver, and 762 bronze, but it's the reputation that's the notable bit!)
A mug with a elastic band wrapped around it (the part where it loops round the handle is hidden from view). The mug has R²/Z² written on it.
LaTeX code. The command is \RandomFractionSum and it takes to arguments. The first specifies a range from 2 to 5, the second specifies two ranges of fractions from 1/12 to 11/12 and then from -11/12 to -1/12.
LaTeX code showing a command that takes in two representations of polynomials in a structured form, with rational coefficients. An example of the representation is {7/5}{1} to denote a term with coefficient 7/5 with the 1 being the power of the unknown.
A solid with a circular cross-section.
3D printed torus in two pieces with the cut along a central möbius strip. In this picture, the pieces are assembled into the torus.
A successful 3D printed model. It's actually of a sliced torus, but that's not the important part.
Two linear sequences laid out one above the other, aligned term by term. The upper sequences is the 17 timestable. The lower is 17n-5. Annotations are added to show how each term in the lower is five less than that in the upper, and how each term across is 17 more than the previous in both sequences. The annotations make commutative squares, much beloved by category theory.
A formula triangle for compound interest, with log_10(100 + overall %) -2 in the top corner, number of years in bottom left, and log_10(100 + APR) - 2 in bottom right.
The final Gaia model. The modules fit together in a cube-based pattern, but then open out to a skeletal octahedral shape with openings and points around it. The modules are made from three patterns, all of small dots on a plain background. One is green dots on white, one lilac on white, one white on purple. This view is through the openings, showing one module of each of three colours.
An old poster advertising a play called "Chalk dust". The background of the poster could be chalk dust on a surface with a dark silhouette which is vaguely circular but with four small cuts in it. The text of the poster reads: Emery Walnut Parkway Nov 9 to 15 8:30pm Seats 25c - 40c "chalk dust" A play in 16 scenes Cast of 40 Cincinnati Federal theatre Wpa Tickets the Henry Strauss-Kahn Co. Inc 6th Walnut
Two copies of the Omega 12 model. The paper has a dotty pattern, but with different base colours of red, green, purple, and pink. The left-hand model uses three colours (not pink) and represents the tricolorabilty of the link. The right-hand model uses all four colors and each link component has a different colour.
A four component link diagram. Start with a 3- set Venn diagram of three overlapping circles, and then overlay a central circle which surrounds the central region but is not so big that it completely contains the pairwise intersections. This is turned into a link diagram by imposing an alternating crossing scheme. Then the diagram is three coloured and that is achieved with no monochrome crossings.
A modular origami model, viewed from above. It uses three patterns of paper, one red with golden baubles, one blue with red and black motifs, and one cream with small red flowers. The modules form darts which appear to meet at their apexes, and at those then four meet of two patterns with opposite modules being the same colour. In the image shown, two blue and two cream modules meet. At the extremities of those darts then red modules are visible descending to the rest of the model.
A trefoil knot made from baked almond dough, decorated with icing that waves back and forth along the path.