Jim Simons
@pippinsboss.bsky.social
Mathematician, tutor of A level maths, bridge player, father, grandfather and dog lover.
Maker of mathematical videos, mostly at the level of A levels
youtube.com/channel/UCnYszOhEIIdIMYyNx2yjwfg
Maker of mathematical videos, mostly at the level of A levels
youtube.com/channel/UCnYszOhEIIdIMYyNx2yjwfg
#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.
w = u + v has the "dimension" function, whereas w(x) = u(x) + v(x) had the "dimension" number.
November 13, 2025 at 10:51 AM
#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.
w = u + v has the "dimension" function, whereas w(x) = u(x) + v(x) had the "dimension" number.
Reposted by Jim Simons
This is fun
youtu.be/dkyvZo68IoM?...
youtu.be/dkyvZo68IoM?...
A Quick Intro to Fiber Bundles (Hopf Fibration)
YouTube video by Richard Behiel
youtu.be
October 25, 2025 at 10:04 AM
This is fun
youtu.be/dkyvZo68IoM?...
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
youtu.be/CUEshWhMJ9c
The Vector Product Done Right
YouTube video by Jim Simons
youtu.be
October 24, 2025 at 7:12 PM
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
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°.
October 20, 2025 at 8:37 AM
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
youtu.be/7jQNTfe-5FM
Zero - The Story of a Number
YouTube video by Jim Simons
youtu.be
October 16, 2025 at 6:44 PM
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
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!
Envelopes and not Envelopes
YouTube video by Jim Simons
youtu.be
September 28, 2025 at 11:42 AM
#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
youtu.be/AneMSG1EO1U
Understanding Envelopes
YouTube video by Jim Simons
youtu.be
September 22, 2025 at 10:59 AM
#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
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.
September 19, 2025 at 9:45 AM
@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.
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.
September 18, 2025 at 12:52 PM
#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.
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 ...
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 ...
August 31, 2025 at 11:45 AM
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 ...
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?
August 27, 2025 at 11:33 AM
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?...
youtu.be/jsW8H76nBKo?...
The Story of the Metre
YouTube video by Jim Simons
youtu.be
August 27, 2025 at 10:55 AM
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?...
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.
August 23, 2025 at 10:18 AM
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, ...
A friend says mathematicians are creative pedants, ...
August 22, 2025 at 3:00 PM
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, ...
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.
August 18, 2025 at 6:52 AM
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
youtu.be/6uaBJq-gd_o
August 17, 2025 at 7:18 PM
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
youtu.be/6uaBJq-gd_o
ξ щ
Stop scrolling and post two characters who bring you joy and happiness.
August 8, 2025 at 3:42 PM
ξ щ
That was a close game!
July 30, 2025 at 9:37 AM
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 do love custom colours in Desmos - I use it a lot when designing graphs that I need to be accessible for students with colour blindness 😁
"I need a fresh color palette." Have you tried math?
Define custom colors in Desmos using HSV or RGB color functions, and use variables and sliders to get just the right look. 🎨
Learn more: help.desmos.com/hc/en-us/art...
#mathsky #iteachmath #mathart
Define custom colors in Desmos using HSV or RGB color functions, and use variables and sliders to get just the right look. 🎨
Learn more: help.desmos.com/hc/en-us/art...
#mathsky #iteachmath #mathart
July 29, 2025 at 11:59 AM
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.
July 18, 2025 at 9:22 AM
I suspect most pea plants are simply connected. Not this one. Cue other mathematically interesting plant pics.
Hurrah!
📢 Exciting News! 🎉
We're thrilled to announce that we will be joining together with other respected mathematics associations to form AMiE (Association for Mathematics in Education).
More information about our transition to AMiE can be found here: buff.ly/6xfmVDv
We're thrilled to announce that we will be joining together with other respected mathematics associations to form AMiE (Association for Mathematics in Education).
More information about our transition to AMiE can be found here: buff.ly/6xfmVDv
July 4, 2025 at 12:54 PM
Hurrah!
This supermarket trolley wheel misunderstood the instructions concerning which axis it is supposed to rotate about.
July 4, 2025 at 11:55 AM
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
youtu.be/Zoib28QEDq4
A Lovely Fact About Pythagorean Triangles
YouTube video by Jim Simons
youtu.be
June 26, 2025 at 6:54 PM
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
youtu.be/Zoib28QEDq4
,3,xhidm66bg66ithh j4dxxdrvxg
June 17, 2025 at 4:04 PM
,3,xhidm66bg66ithh j4dxxdrvxg
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.
June 8, 2025 at 3:09 PM
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.