Segar Rogers
@segarrogers.bsky.social
/sē′gər/ Teacher. Maths. Secondary. Edinburgh. Old enough to remember chalk. Currently taking a sabbatical. Occasional poetry.
I like this a lot … feels so uncomplicated … expanding the brackets (in this situation) just feels overkill. #UKMathsChat
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
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
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
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
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
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
Anyone know what this is called? Is it a thing?! Found it in Bīrūnī from the 11th century ... as one does. #UKMathsChat #iTeachMath
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
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.
Segar Rogers@segarrogers.bsky.social · 6mo agoThis 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
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
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
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
From @mosababutoha.bsky.social's book, Things You Might Find Hidden in My Ear: bookshop.org/a/862/9780872868601 #poem #books #writing
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
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.
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
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
Michael Pershan@mpershan.bsky.social · 8mo agoToday I learned that this just works.
#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.
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!!
Wondering about the parallels (if any) in other disciplines.
Matthew Stewart@roguestrands.bsky.social · 10mo agoPoetry in English possesses two separate but intertwined beats. First of all, the stresses. And secondly, underneath those stresses, the syllables. The subtle latter are often drowned out by the strident former. But if you listen hard enough, the syllabics are there, underpinning everything.
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
Does anyone teach this? Wondering if it's generally known or generally not known. #UKMathsChat #iTeachMaths
An hour in the wind this afternoon collecting an oak forest :-)
#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 ;-)