Indeed, some scholars have argued that some early Homo species should be reclassified as Australopithecus.

I'm self-employed, so I have to fill in a tax form every year, and I have a guilty secret - because it is all numbers and spreadsheets, I rather enjoy doing it.

In #Mathstoday, we explored 2D linear transformations. I made this geogebra thingy, but the coordinates of the transformed points only seem to be right to about 2sf, even when the matrix is the identity. Am I doing something silly? www.geogebra.org/m/regvfyr2

#ukmathschat calculator hack. My calculator app can convert between units, such as gallons and litres. To convert pence per litre to pence per gallon, convert from gallons to litres.

As a programmer back in the day, I sometimes faced the "come from" problem. A program crashed executing code it should never have reached: how did it get there? Today I have a different come from problem. We have been sent flowers by Margaret. We know many Margarets ...

In #Mathstoday, I realised there are three ways a Venn diagram can be used. Each region can be labelled with its probability, OR the number of outcomes, OR the actual outcomes. The last two can be confused if the outcomes are positive inegeters. (A student was confused on that point, briefly.)

360 assembler soldering with a blow lamp drop kicking a rugby ball valve grinding remembering my friends' telephone numbers

In #MathsToday, one of my students missed his lesson because it was his birthday: his 70th birthday! He did tell me in advance though.

Met a new student in #MathsToday, an economics graduate who wants to retake #ALevelMaths, working largely on his own. He was having difficulty with trig equations and CAST. He had learnt the trig graphs, so I told him to cast CAST aside, and showed him how to solve these properly - he was SO happy!

Just been looking at new televisions. The power consumption is measured in kWh per 1000 hours. Err, I make that Watts.

Today we went to "the finest tapas bar in Worcestershire". Hhm, I wonder how much competition there is for that accolade. Actually it was really good.

#mathstoday I'm teaching a retired chemistry teacher, and we are into functions as elements of a vector space. It's been help to think in terms of dimensional analysis. Ie if u, v and w are functions, w = u + v has the "dimension" function, whereas w(x) = u(x) + v(x) had the "dimension" number.

This is fun youtu.be/dkyvZo68IoM?...

I don't suppose anyone of the illustrious company I find myself amongst here need any help with the vector product, but teaching it recently I consulted several textbooks, all of which, it seems to me, have it arsy-versy, so I've made a video about doing it right. youtu.be/CUEshWhMJ9c

All you maths linguists out there. Is there a word for angles less than 180°? Like 0° < acute < 90° < obtuse < 180° < reflex < 360°.

If you don't know the history of zero, here's an explainer to get you up to speed with a fascinating story. Really there are two zeros: zero the digit and zero the number. So I start by exploring ancient number systems that had one or the other or both or neither. youtu.be/7jQNTfe-5FM

#ALevelMaths In my previous video I looked at how to work out the equation for the envelope of a family of curves. This time I look at some situations here that method comes up with something that isn't an envelope. Enjoy!

#AlevelMaths Envelopes appear in Further Maths, at least for Edexcel and OCR/MEI, and the formula for an envelope is a bit mysterious, so I've been digging into it, and have made a video you might enjoy. youtu.be/AneMSG1EO1U

@davidkbutler.bsky.social It is a magnificent Autumn for berries here in the UK. Just look at this spindle bush in a field near my home.

#MathsToday #AlevelMaths The Edexcel spec talks about 1-1 or many-1 functions and 1-many mappings, but doesn't mention many-many mappings. One of my pupils reports that his teacher says "you can't have many to many mappings". Well you certainly can, though perhaps not in an Edexcel exam.

I'm exploring envelopes, in the mathematical sense, which have always puzzled me. It's not a corner of mathematics I've hade reasons to study before. If f(t,x,y)=0 is a family of curves, t being a parameter, I follow the proof that we obtain an equation for the envelope ...

The brewers of Proper Job beer have produced a strong IPA called Big Job. When I was toddler, doing a big job was a euphemusm for having a crap. These things change rapidly, so presunably the brewery employs nobody young enough to remember this. Should I tell them?

I've published my latest video, on the history of the metre, focussing on the aspects of the history that as a mathematician I find particularly interesting. For example, do you know which unit is now defined to be an irrational multiple of a metre? youtu.be/jsW8H76nBKo?...

Gosh, I've been slow. I've only just realised that the fact that 100 kilometres is almost exactly 54 nautical miles is not a coincidence. A nm was originally 1 arc minute around a great circle on the Earth, and a km was originally 1/10000 of the distance from the North pole to the equator via Paris.

There was a recent thread on pedantry in mark schemes, which prompts a thought on pedantry in mathematics. In brief there are two sorts, one good, one a pain. A friend says mathematicians are creative pedants, ...

The hedgrows round here are festooned with red haws, blue sloes and blackberries to an extent I don't remember ever seeing before.

Do you remember the rod, pole or perch, and do you wonder where they come from? Ever wondered where the strange factor of 11 comes from in the number of yards in a mile. All is revealed in my latest video: youtu.be/6uaBJq-gd_o

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That was a close game!

Is there a standard set of colours to use that will work for people with various forms of colour blindness? For use, eg, when I'm making a video, when of course I don't know who will watch. I have in mind something that says "If you need five contrasting colours, here are the ones to use".

I suspect most pea plants are simply connected. Not this one. Cue other mathematically interesting plant pics.

Hurrah!

This supermarket trolley wheel misunderstood the instructions concerning which axis it is supposed to rotate about.

Did you know that the inradius, and all three exradii, of a Pythagorean triangle are all integers? Here is a video exploring this delightful fact via Heron's formula for the area of a triangle and Euclid's formula for generating primitive pythagorean triples. youtu.be/Zoib28QEDq4

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Next year I am going to do some maths olympiad coaching, which I am really looking forward to. Does anyone have any books or other resources to recommend, apart from past papers of course.

There is something evocative (of what I'm not sure) about the light of a summer's evening. I guess it has to do with the prolonged twilight. This year, I noticed it for the first time this evening, walking home from the pub.

The new pope has a maths degree, and is clearly an intellectual heavyweight. I googled "mathematician pope", and it offered me Sylvester II who pontificated 999 to 1003. Fascinating guy, and like Leo, quite the intellectual. I wonder if Robert Prevost considered calling himself Sylvester V.

Pray tell me, Dr Fermi, how many flowers do you think there are on my wisteria.

This is fun.

Granddaughter has always loved rainbows. We made a rainbow-themed picnic for her 12th birthday. Note the black things at the end. They represent ultraviolet!

Our fritillaries are very happy by the pond.

#MathsToday #AlevelMaths Fruitful discussion prompted by two flawed questions. One says "... equilibrium ... find the coefficient of friction". It doesn't say limiting friction or anything to imply that, so actually we can only find a lower bound on μ.

There's another one: QEA, quod est absurdum, to be used at the of a proof by contradiction. Have you ever met that?

#MathsToday #ALevelMaths My student tackled an integration problem that ended up with a cubic to be solved. She has a new calcualtor, and hasn't yet worked out how to use it to solve cubics, so she used Newton-Raphson. Hurrah!

#MathsToday Newton-Raphson. I love it. I often complain about daft questions in the text book, but thus is great. Kepler's equation. Though it doesn't mention Kepler by name, it says "an astronmer" and "a planet" with eccentricity 0.1. That's Mars. It is often said that Kepler showed that. ..

#MathsToday Newton Raphson. I love it. I often complain about Qs in the text book, but this is brilliant. Kepler's equation. It talks about "an astronomer", and "a planet" with eccentricuty 0.1. That's Mars. It is often said the Kepler showed that the planets move in ellipctical orbits.

My electric car has a dial labelled consumption, in miles per kilwatt-hour, instantaneous and long-term average. That's a strange unit, but it has the dimensions of force^(-1), so it must really be showing the driving force! So let's convert my long term average, 4.1, to Newtons. ...

Mathematics in School in shreds. Does anyone want a dog?

Looks like I forgot to attach the photo