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
Let a typical quadrilateal be a (0,0), (1,0), (a,b) & (c,d). Let the decimal expansion of a be
...a_2 a_1 a_0 . a_(-1) a_(-2)
Etc
Map this quadrilateral to the triangle at (0,0),(1,0) (p,q) where the decimal expansion of p is
...a_1 c_1 a_0 c_0 . a_(-1) c_(-1) a_(-2)
and similary for q.
...a_2 a_1 a_0 . a_(-1) a_(-2)
Etc
Map this quadrilateral to the triangle at (0,0),(1,0) (p,q) where the decimal expansion of p is
...a_1 c_1 a_0 c_0 . a_(-1) c_(-1) a_(-2)
and similary for q.
November 13, 2025 at 6:50 PM
Let a typical quadrilateal be a (0,0), (1,0), (a,b) & (c,d). Let the decimal expansion of a be
...a_2 a_1 a_0 . a_(-1) a_(-2)
Etc
Map this quadrilateral to the triangle at (0,0),(1,0) (p,q) where the decimal expansion of p is
...a_1 c_1 a_0 c_0 . a_(-1) c_(-1) a_(-2)
and similary for q.
...a_2 a_1 a_0 . a_(-1) a_(-2)
Etc
Map this quadrilateral to the triangle at (0,0),(1,0) (p,q) where the decimal expansion of p is
...a_1 c_1 a_0 c_0 . a_(-1) c_(-1) a_(-2)
and similary for q.
In the sense of cardinality, the same number, but in terns of dimension, triangles form a 3-dimensional manifold whereas quadrilaterals form a 5-dimensional one.
November 12, 2025 at 10:39 PM
In the sense of cardinality, the same number, but in terns of dimension, triangles form a 3-dimensional manifold whereas quadrilaterals form a 5-dimensional one.
I'm no wizard, and I'm not sure if this what you want, but you can reference a cell in another workbook, as in
=[thotheotherbokbook.xlsx]Sheet1!$b$12.
=[thotheotherbokbook.xlsx]Sheet1!$b$12.
November 10, 2025 at 6:25 PM
I'm no wizard, and I'm not sure if this what you want, but you can reference a cell in another workbook, as in
=[thotheotherbokbook.xlsx]Sheet1!$b$12.
=[thotheotherbokbook.xlsx]Sheet1!$b$12.
I'm in danger of coming cross as a grumpy old man here, but that first one, for example, really ought to be
EITHER
-1 < sin x < 1, 0 <= x <= 360˚
OR
-1 < sin x˚ < 1, 0 <= x <= 360
Depending upon whether you want to think of x as an angle or a number.
EITHER
-1 < sin x < 1, 0 <= x <= 360˚
OR
-1 < sin x˚ < 1, 0 <= x <= 360
Depending upon whether you want to think of x as an angle or a number.
November 4, 2025 at 8:34 PM
I'm in danger of coming cross as a grumpy old man here, but that first one, for example, really ought to be
EITHER
-1 < sin x < 1, 0 <= x <= 360˚
OR
-1 < sin x˚ < 1, 0 <= x <= 360
Depending upon whether you want to think of x as an angle or a number.
EITHER
-1 < sin x < 1, 0 <= x <= 360˚
OR
-1 < sin x˚ < 1, 0 <= x <= 360
Depending upon whether you want to think of x as an angle or a number.
NIce! But one is also using associativity. Multiplication is a binary operation and so 5×3 has a meaning, 3×2 has a meaning, and so (5×3)×2 and 5×(3×2) have meanings. Associativity says these are the same, and allows us to write 5×3×2 for either, which without associativity would be meaningless.
October 28, 2025 at 10:11 PM
NIce! But one is also using associativity. Multiplication is a binary operation and so 5×3 has a meaning, 3×2 has a meaning, and so (5×3)×2 and 5×(3×2) have meanings. Associativity says these are the same, and allows us to write 5×3×2 for either, which without associativity would be meaningless.
I hadn't looked at the video when I talked about the nice solutions that appeared here. I must say all the video solutions are pretty unattractive, but they certainly show that there are many ways to tackle the problem.
October 27, 2025 at 5:42 PM
I hadn't looked at the video when I talked about the nice solutions that appeared here. I must say all the video solutions are pretty unattractive, but they certainly show that there are many ways to tackle the problem.
You've always got the remember what the private sector is efficient AT, namely making money out its customers. When the customer is the government ...
October 27, 2025 at 9:49 AM
You've always got the remember what the private sector is efficient AT, namely making money out its customers. When the customer is the government ...
That's also very pretty. So many lovely, but completely different, approaches.
October 27, 2025 at 3:54 AM
That's also very pretty. So many lovely, but completely different, approaches.
I got there by rotating UQ by π/4 and shrinking it by √2 to find V, (in show-off mode I did this using complex numbers), then setting a determinant to 0 to check when V, S and Q are collinear.
October 26, 2025 at 4:18 PM
I got there by rotating UQ by π/4 and shrinking it by √2 to find V, (in show-off mode I did this using complex numbers), then setting a determinant to 0 to check when V, S and Q are collinear.
That was excelkent' but now I have a Beach Boys song running round in my head witth new words...I'm Picking up Hopf Fibations
October 25, 2025 at 4:20 PM
That was excelkent' but now I have a Beach Boys song running round in my head witth new words...I'm Picking up Hopf Fibations
That's interesting, and I imagine it is mostly done the right way round at university level, but at least here in England it seems to be done the wrong way round at school.
October 24, 2025 at 7:38 PM
That's interesting, and I imagine it is mostly done the right way round at university level, but at least here in England it seems to be done the wrong way round at school.
In the unlikely event that you'd like to use the geogebra app that appears in the video, here it is.
www.geogebra.org/m/vtwcqj3x
www.geogebra.org/m/vtwcqj3x
Vector Product Done Right
Vector Product
www.geogebra.org
October 24, 2025 at 7:21 PM
In the unlikely event that you'd like to use the geogebra app that appears in the video, here it is.
www.geogebra.org/m/vtwcqj3x
www.geogebra.org/m/vtwcqj3x
How fascinating! How varied humanity is.
October 24, 2025 at 7:20 PM
How fascinating! How varied humanity is.
Me too, and I actually turned a bicyle inner tube inside out!
October 21, 2025 at 10:53 PM
Me too, and I actually turned a bicyle inner tube inside out!
I'm happy to have spread a little bit of vocabulary-based joy in one little corner of cyberspace.
October 21, 2025 at 10:44 PM
I'm happy to have spread a little bit of vocabulary-based joy in one little corner of cyberspace.
I've discovered some people call it a convex angle, which makes some sense, although it suggests a reflex angle should be called concave.
Incidentally, did you know that angles that add uo to 360° are called explementary?
Incidentally, did you know that angles that add uo to 360° are called explementary?
October 20, 2025 at 9:47 PM
I've discovered some people call it a convex angle, which makes some sense, although it suggests a reflex angle should be called concave.
Incidentally, did you know that angles that add uo to 360° are called explementary?
Incidentally, did you know that angles that add uo to 360° are called explementary?
Well I'm sure that's true in general, but for the purpose I have in mind, I want a word that means acute-or-obtuse or not-reflex.
October 20, 2025 at 10:03 AM
Well I'm sure that's true in general, but for the purpose I have in mind, I want a word that means acute-or-obtuse or not-reflex.
Looks like mistletoe to me. Google ai tells me that mistletoe is rare in Ireland, but that that botanic park is one if the places it is found. It distribution in GB is interesting and patchy.
October 20, 2025 at 2:58 AM
Looks like mistletoe to me. Google ai tells me that mistletoe is rare in Ireland, but that that botanic park is one if the places it is found. It distribution in GB is interesting and patchy.
The symmetries of Things by Conway et al.
October 18, 2025 at 7:26 AM
The symmetries of Things by Conway et al.