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Segar Rogers @segarrogers.bsky.social · 27/09/2026

Seeing number patterns in other bases : the square of 13 is half the sum of the squares of 7 and 17 … more visible in sexagesimal than decimal. I like the idea that 4000 year old cultures (with base 60) could see certain things more easily than we can. Brings to mind the Sapir-Whorf Hypothesis.

A table of values 6 to 18 and their squares ... in sexagesimal.

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Segar Rogers @segarrogers.bsky.social · 26/09/2026

An Old Akkadian school text problem; only 4000 years old. I think they were interested in how to partition non-rectangular fields for inheritance purposes ... so for 2 brothers say, in the case of this problem. #UKMathsChat #iTeachMath

Old Akkadian school text IM 58045 showing a trapezium partitioned into two equal areas. The parallel sides of the trapezium are 17 and 7 units and the perpendicular distance between these sides is 12 units. The partition is made parallel to the sides of 17 and 7 units. Find the length of the partition line and its distance from the side of 17 units.

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Segar Rogers @segarrogers.bsky.social · 17/09/2026

Worth perhaps sharing my own approach. (As pointed out by Catriona Agg the 6 is superfluous – an unintended error on my part). #UKMathsChat #iTeachMaths

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Segar Rogers @segarrogers.bsky.social · 14/09/2026

Surveyor's Tradition Problems. Q1&2 are similar, Q3&4 are similar, etc, etc. Always a risk writing resources when you're no longer in the classroom to experience the outcome (be it glory or mayhem) ... but hopefully this is of use or of interest to some. #UKMathsChat #iTeachMath

Sets 1 and 2 of a collection of area-length problems.

Set 3 of a collection of area-length problems.

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Segar Rogers @segarrogers.bsky.social · 11/09/2026

I think the maths historians would probably call this a 'surveyors' problem. Am in the process of making a sheet of them ... unless anyone already has such a thing. (The 40 and the 72 are the areas of the rectangles formed by the respective diagonals). #UKMathsChat #iTeachMath

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Segar Rogers @segarrogers.bsky.social · 09/09/2026

An idea for a question: Without recourse to calculators, tables or graphing packages: a) Place sec x, cos x, tan x, cot x, csc x & sin x in order, from smallest to largest, when x = 1°. b) How is this different for x = 44° ? #UKMathsChat

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Segar Rogers @segarrogers.bsky.social · 10/06/2026

Algebra is the arithmetic of unknowns.

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Segar Rogers @segarrogers.bsky.social · 09/06/2026

I like this a lot … feels so uncomplicated … expanding the brackets (in this situation) just feels overkill. #UKMathsChat

Four examples showing how transformation of the minuend and subtrahend in a subtraction can simplify an expression.

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Segar Rogers @segarrogers.bsky.social · 08/06/2026

Piecing together thought processes for 9th century algebra … in the absence of a) symbolic algebra and b) negative numbers: now: simplify 14 − (10 − x) then: simplify [14] less [10 less x] minuend: [14] subtrahend: [10 less x] • goal: ... 1/3 #UKMathsChat #iTeachMath #historyofmaths

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Segar Rogers @segarrogers.bsky.social · 01/06/2026

Pre-algebra simultaneous equations. Clever! 盈不足術 /yíng bù zú shù/ rule of too much and not enough (!) حساب الخطأين /ḥisāb al-khaṭa'ayn/ reckoning from two falsehoods regula duorum falsorum rule of double false position Subtract if both guesses are deficits/excesses. #historyofmaths #UKMathsChat

A table showing how to solve the pair of equations 2x+3y=19 and 5x+2y=31 by using the method of double false position.

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Segar Rogers @segarrogers.bsky.social · 28/05/2026

So I'm reading about the origins of algebra ... and I find this from Abū Kāmil in about 900CE ... and of course Kāmil's algebra (al-jabr!) could solve this. Pretty amazing really. #UKMathsChat #iTeachMath

$Upper half of image displays the text of Abū Kāmil's Problem 3: "So if he said ten: you divided it into two parts. So you divided each one of them by the other. Then you subtracted one of them from the other, so there remained five-sixths of a dirham". Lower half gives this rendered in modern algebra: \frac{x}{10-x} - \frac{10-x}{x} = \frac{5}{6}$

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Segar Rogers @segarrogers.bsky.social · 26/05/2026

Euclid Elements Book II Proposition 5 Intriguingly this was used by the Egyptian mathematician Abū Kāmil in the 10th century to solve quadratic equations of the form x² + 21 = 10x #UKMathsChat #iTeachMath

Two diagrams illustrating the same relationship. Both show a line AB with a midpoint M and a further cut C (positioned differently in each diagram). Squares and rectangles constructed around various line segments provide a graphical illustration of the relationship AC×CB + MC² = MB².

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Segar Rogers @segarrogers.bsky.social · 07/05/2026

I'm looking for a publisher. 240 pages of old-world trigonometry, geometry focused & algebra free – where it came from, who built it, how they built it, how they used it, and how to do trigonometry in this way today. Any suggestions gratefully received. #UKMathsChat #iTeachMath #MathSky

A selection of twelve indicative thumbnail pages arranged in a grid.

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Segar Rogers @segarrogers.bsky.social · 22/04/2026

Semiotic observation (!) ... when you think of the Inscribed Angle Theorem, which arc do you mentally highlight? I've always done (a) but actually Euclid presents it as (b) … which makes sense because the angles are indeed in that segment. Time on my hands? Maybe ;-) #UKMathsChat #iTeachMath

Two diagrams showing the Inscribed Angle Theorem. On the left the minor arc is highlighted; on the right the major arc is highlighted. Text reads: Euclid El, 3–21 'In a circle, angles in the same segment are equal to one another'.

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Segar Rogers @segarrogers.bsky.social · 26/02/2026

Anyone know what this is called? Is it a thing?! Found it in Bīrūnī from the 11th century ... as one does. #UKMathsChat #iTeachMath

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Segar Rogers @segarrogers.bsky.social · 20/02/2026

I’m thinking of buying a visualiser … either an IPEVO DO-CAM or an Innex DC500. If you use either of these I’d love to hear your views of them … particularly any shortcomings. #UKMathsChat #iTeachMath

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Segar Rogers @segarrogers.bsky.social · 19/02/2026

There were no takers for this … but here's the solution for completeness. It's all similar triangles ... with some fancy ratio table moves; the reductions come from common diagonals in the upper pair … and common columns in the bottom pair. Classical moves that we're maybe less familiar with today.

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Segar Rogers @segarrogers.bsky.social · 13/02/2026

Lovely proportional reasoning from a pupil I tutor. She couldn't remember if she'd been taught similar triangles … but said: since 3 is less than half of 7, then AB will be less than half of 10.5 … and (red lines hers) if we split the 10.5 into 7 parts then AB will be 3 of these parts. #MathsToday

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Segar Rogers @segarrogers.bsky.social · 08/02/2026

Still messing around with ratio tables. The marking scheme for this question (SQA N5M 2024 P2) focuses on the Sine Rule ... but a similar triangles approach does the job nicely ... and the ratio table bypasses any worries with algebraic manipulation. #UKMathsChat #iTeachMath

Question 13 from the 2024 SQA National 5 Maths Paper 2 exam (worth 5 marks) ... with my annotated workings using similar triangles and a ratio table.

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Segar Rogers @segarrogers.bsky.social · 06/02/2026

Proof of cot θ × tan θ = 1 … using the Out-In Complementary Principle. #UKMathsChat #iTeachMath

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Segar Rogers @segarrogers.bsky.social · 02/02/2026

This is the geometry in one of the diurnal problems from Brahmagupta's 7th century Khandakhādyaka. I've undertaken some repositioning to aid the aesthetic, and a little obfuscation to add to the challenge. #UKMathsChat #iTeachMath

Six straight lines forming 3 triangles. Two angles are marked as equal. Two lengths are marked as equal. Find the missing length.

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Reposted by Segar Rogers

Litbowl @litbowl.bsky.social · 02/02/2026

From @mosababutoha.bsky.social's book, Things You Might Find Hidden in My Ear: bookshop.org/a/862/9780872868601 #poem #books #writing

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Segar Rogers @segarrogers.bsky.social · 30/01/2026

Still in ratio table mode. I remembered this @mathforge.org ;-)

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Segar Rogers @segarrogers.bsky.social · 25/01/2026

Some 'aspects/rules' of ratio tables ... collected together as an aid to proportional reasoning. 'El. V–16' = Euclid's Elements Book 5 Proposition 16 #UKMathsChat #iTeachMath

Nine 'rules' of ratio tables laid out in a 3 by 3 grid format.

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Segar Rogers @segarrogers.bsky.social · 23/01/2026

Related ratio tables?? Find what can be found. #UKMathsChat

Two ratio tables sharing a common diagonal of unknown values. The second table contains a further unknown value.

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Segar Rogers @segarrogers.bsky.social · 22/01/2026

A diagram for a diagram-less tradition; gradually making some sense of Brahmagupta's Khandakhadyaka. With a couple of shadow measurements and the angle of the rising sun he could calculate the time of day. Astonishing really.

A cross-section of the celestial sphere annotated with transliterated Sanskrit terminology.

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Segar Rogers @segarrogers.bsky.social · 13/12/2025

Where would you give the marks here? It depends how you do your trigonometry of course. But if you teach it via a similar triangles approach I can only find 3 marks. Is there even a 4th mark (with this approach)? (2003 Scottish Credit Paper 2 – 4 marks). #UKMathsChat #iTeachMaths

A right-angled triangle with angle 34°, hypotenuse 13.1cm. Also a second right-angled triangle with angle 25° whose hypotenuse is joined to the opposite side of the first triangle. Find the adjacent side of the 25° right-angled triangle.

My solution based on scaling a 1-sin θ-cos θ unit triangle twice, first by 13.1 and then by 13.1 sine 34°. Answer is 6.64 2d.p,

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Segar Rogers @segarrogers.bsky.social · 12/12/2025

Apologies for jumping out of the thread … interested in conceptual explanations accessible to pupils. My take: 8/21 ÷ 4/3 8 twentyoneths ÷ 4 thirds So 4 thirds into 8 twentyoneths 4 goes into 8 twice. A third goes into a twentyoneth 'a seventh' times. So 2 × (1/7) So 2/7 @germinalmaths.bsky.social

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Segar Rogers @segarrogers.bsky.social · 07/12/2025

#poetry Anna Akhmatova, trans. Kunitz and Haywood. Akhmatova lived in Tashkent in the early 40’s. Termez lies to the south, on the border of Uzbekistan and Afghanistan. I go through phases with poetry … it’s been a while … for the last week or so I’ve felt it calling … specifically Akhmatova.

Poem. “Your Lynx-Eyes, Asia . . . “ by Anna Akhmatova.

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Segar Rogers @segarrogers.bsky.social · 04/12/2025

Euclid's Dedomena/Data. 94 'If A is given then B is also given' propositions. The Data proves only whether relationships exist: 'If in a circle given in magnitude a straight line be drawn cutting off a segment admitting a given angle, the line drawn is given in magnitude.' – that's trigonometry!!

Book Cover: 'Euclid's Data' by Christian Marinus Taisbak

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Segar Rogers @segarrogers.bsky.social · 04/11/2025

Wondering about the parallels (if any) in other disciplines.

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Segar Rogers @segarrogers.bsky.social · 03/11/2025

Trying to write a question that requires the use of the Angle Bisector Theorem (Eu. El. VI – 3) … but failing … somehow a non VI – 3 solution always presents itself. Still, ended up with a nice enough question. #UKMathsChat #iTeachMaths

A circle with an arrangement of chords. One chord bisects two others. Three lengths are given

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Segar Rogers @segarrogers.bsky.social · 01/11/2025

Does anyone teach this? Wondering if it's generally known or generally not known. #UKMathsChat #iTeachMaths

A triangle with the apex angle bisected and drawn to the base ... partitioning the base into lengths 6 (left) and 8 (right). The sloping sides are 9 (left) and x (right). Find x.

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Segar Rogers @segarrogers.bsky.social · 25/10/2025

An hour in the wind this afternoon collecting an oak forest :-)

The inside of an orange sunlit polythene bag containing many acorns.

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Segar Rogers @segarrogers.bsky.social · 23/10/2025

#MathsToday Looking through the jotter of a girl I’m tutoring … today’s page … the first two trig identities … below one the word ‘Tesco’ … below the other ‘Scone’. Just when you think you’ve seen everything. I’ll leave you to work out which is which ;-)

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Segar Rogers @segarrogers.bsky.social · 22/10/2025

When you're teaching integration by substitution, what do you tell pupils is going on (conceptually)? Interested in the phrases people use ... and I appreciate you may just take a procedural route. #UKMathsChat #iTeachMaths

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Segar Rogers @segarrogers.bsky.social · 20/10/2025

Been thinking more about the merits of the Exterior Angle Theorem and the fluency of pupils' geometric thinking. Here's a proof of one of @karencampe.bsky.social 's angle–arc theorems. Step 4 is beautifully immediate _if_ one uses Exterior-Angle-Theorem thinking. #UKMathsChat #iTeachMaths

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Segar Rogers @segarrogers.bsky.social · 13/10/2025

Left: Requires triangle-interior-angle-sum and straight-angle-sum. 3 steps. Slower? Right: Exterior Angle Theorem (Euclid 1–32). Requires corresponding and alternate angles. 1 step. Faster? Right feels cleaner to me ... I wonder what pupils would think? #UKMathsChat #iTeachMaths

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Segar Rogers @segarrogers.bsky.social · 11/10/2025

What things in maths do we teach before we have taught the maths that shows it is true? #UKMathsChat #iTeachMaths

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Segar Rogers @segarrogers.bsky.social · 09/10/2025

A very short primer on mixing degrees of arc with degrees of angle for circle theorems. #UKMathsChat #iTeachMath Historically degrees measured arcs and arcs measured angles. This might feel uncomfortable but remember how we measure an angle today … with a protractor … measuring around an arc. 1/6

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Segar Rogers @segarrogers.bsky.social · 21/09/2025

Idle thought: Explain in a sentence why for any numbers n and s such that n>s, s²/n is closer to s than n is . #UKMathsChat

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Segar Rogers @segarrogers.bsky.social · 15/09/2025

Idle thought: Explain geometrically why the square-root operator is distributive over multiplication. #UKMathsChat

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Segar Rogers @segarrogers.bsky.social · 14/06/2025

An aide-memoire for right-angled trig?! … maybe not … but it's interesting how orientation affects our ability to remember relationships. In this orientation I find the symmetry of the relationships much clearer. If only all trig questions had horizontal hypotenuses ;-) #UKMathsChat #iTeachMaths

Three right-angled triangles, each with a different side labelled one unit, with the other sides labelled in terms of sine and tangent.

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Segar Rogers @segarrogers.bsky.social · 05/06/2025

An Ailles Rectangle problem. Find the value of a°. More an exercise in (trigonometry) language fluency than anything else. i.e. do you know how to interpret the terminology to be able to do it in your head. @davidkbutler.bsky.social #UKMathsChat #iTeachMaths

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