Segar Rogers
@segarrogers.bsky.social
Teacher. Maths. Secondary. Edinburgh.
Old enough to remember chalk.
Poetry on a Sunday.
Old enough to remember chalk.
Poetry on a Sunday.
I never tire of this :-)
November 29, 2025 at 8:33 PM
I never tire of this :-)
Came up with this ... but then noticed it might be the same as your Heron's shortest path argument?
– The dashed line is the shortest route from A to B.
– Which is the longer route: via C or via D?
– The dashed line is the shortest route from A to B.
– Which is the longer route: via C or via D?
November 28, 2025 at 10:24 PM
Came up with this ... but then noticed it might be the same as your Heron's shortest path argument?
– The dashed line is the shortest route from A to B.
– Which is the longer route: via C or via D?
– The dashed line is the shortest route from A to B.
– Which is the longer route: via C or via D?
A variation on the ellipse argument:
– Imagine two slings of different lengths.
– One supports the red disc.
– The other supports the blue disc.
– They are held in the positions shown ...
– ... and then released.
– Which will swing the lowest?
– Imagine two slings of different lengths.
– One supports the red disc.
– The other supports the blue disc.
– They are held in the positions shown ...
– ... and then released.
– Which will swing the lowest?
November 28, 2025 at 9:51 PM
A variation on the ellipse argument:
– Imagine two slings of different lengths.
– One supports the red disc.
– The other supports the blue disc.
– They are held in the positions shown ...
– ... and then released.
– Which will swing the lowest?
– Imagine two slings of different lengths.
– One supports the red disc.
– The other supports the blue disc.
– They are held in the positions shown ...
– ... and then released.
– Which will swing the lowest?
I’m not sure this is in the spirit of your question … but I thought about the sum of the squares on each triangle:
L = 3² + 4² + (3² + 4²)
R = 3² + (1² + 4²) + (2² + 4²)
… leaving you to decide which is bigger: 1² + 2² or 3².
L = 3² + 4² + (3² + 4²)
R = 3² + (1² + 4²) + (2² + 4²)
… leaving you to decide which is bigger: 1² + 2² or 3².
November 28, 2025 at 8:30 PM
I’m not sure this is in the spirit of your question … but I thought about the sum of the squares on each triangle:
L = 3² + 4² + (3² + 4²)
R = 3² + (1² + 4²) + (2² + 4²)
… leaving you to decide which is bigger: 1² + 2² or 3².
L = 3² + 4² + (3² + 4²)
R = 3² + (1² + 4²) + (2² + 4²)
… leaving you to decide which is bigger: 1² + 2² or 3².
I’ve always struggled with the way the powers-that-be wanted ‘evidence’ of anything I’ve wanted to implement … but when they’ve wanted to implement something, ‘evidence’ doesn’t seem to be required.
November 22, 2025 at 7:24 PM
I’ve always struggled with the way the powers-that-be wanted ‘evidence’ of anything I’ve wanted to implement … but when they’ve wanted to implement something, ‘evidence’ doesn’t seem to be required.
I’m confused. Degrees are a measure arc length … and arc length is a measure of angles (Edmund Gunter, 1624). So a circle is indeed 360° (of arc length) … is the ‘of arc length’ not implicit?! I’m not sure the examiners know their history ;-)
November 10, 2025 at 10:37 PM
I’m confused. Degrees are a measure arc length … and arc length is a measure of angles (Edmund Gunter, 1624). So a circle is indeed 360° (of arc length) … is the ‘of arc length’ not implicit?! I’m not sure the examiners know their history ;-)
A point for making me laugh ;-)
November 8, 2025 at 6:14 PM
A point for making me laugh ;-)
Yes. Very nice. More of this :-)
November 5, 2025 at 7:10 PM
Yes. Very nice. More of this :-)
I’m drawn to the idea of two aesthetics, one in the foreground, one in the background … and trying to meld that idea with another discipline, such as mathematics (which is my disciple). I appreciate I may be reaching ;-)
November 4, 2025 at 3:15 PM
I’m drawn to the idea of two aesthetics, one in the foreground, one in the background … and trying to meld that idea with another discipline, such as mathematics (which is my disciple). I appreciate I may be reaching ;-)
It’s a good question though; how indeed did they do it back in the day before trig substitutions? Be interesting to look up if Cavalieri or similar had a solution.
November 4, 2025 at 12:18 PM
It’s a good question though; how indeed did they do it back in the day before trig substitutions? Be interesting to look up if Cavalieri or similar had a solution.
lol … okay I feel myself reacting to this too! … are these ‘tricks’ not standard proof techniques with very definite logical foundations?! … should we not use their names and embrace the wonder that they are?! Wasn’t first order logic built to ensure our proof techniques are well founded?!
November 3, 2025 at 3:47 PM
lol … okay I feel myself reacting to this too! … are these ‘tricks’ not standard proof techniques with very definite logical foundations?! … should we not use their names and embrace the wonder that they are?! Wasn’t first order logic built to ensure our proof techniques are well founded?!
I’m wondering if the sine rule is overkill. The proof requires an alternate angle, a corresponding angle, a property of isosceles triangles, and then similar triangles.
(I suppose it depends on how good a pupil’s geometry is … relative to how good pupil’s trigonometry is.)
(I suppose it depends on how good a pupil’s geometry is … relative to how good pupil’s trigonometry is.)
November 2, 2025 at 12:51 PM
I’m wondering if the sine rule is overkill. The proof requires an alternate angle, a corresponding angle, a property of isosceles triangles, and then similar triangles.
(I suppose it depends on how good a pupil’s geometry is … relative to how good pupil’s trigonometry is.)
(I suppose it depends on how good a pupil’s geometry is … relative to how good pupil’s trigonometry is.)
Good question … and I can’t decide. Euclid’s proof of this is lovely, so maybe there is merit in looking at it for that reason. But then is it worth spending time on something that is rarely used? (Euclid does use it in the Data to be fair). Yeah, I don’t have a strong view either way on this one.
Euclid's Elements, Book VI, Proposition 3
mathcs.clarku.edu
November 2, 2025 at 9:27 AM
Good question … and I can’t decide. Euclid’s proof of this is lovely, so maybe there is merit in looking at it for that reason. But then is it worth spending time on something that is rarely used? (Euclid does use it in the Data to be fair). Yeah, I don’t have a strong view either way on this one.
I’ll put my mind to a more extended question ;-)
November 1, 2025 at 10:07 PM
I’ll put my mind to a more extended question ;-)
Mass point geometry … I had to look it up … intriguing! :-)
November 1, 2025 at 10:01 PM
Mass point geometry … I had to look it up … intriguing! :-)
I'm wondering what assessment questions look like that require this ... just basic 'do you know it' questions (like my graphic)? ... or more complex, involving the use of this to then allow you to find something else?
November 1, 2025 at 7:31 PM
I'm wondering what assessment questions look like that require this ... just basic 'do you know it' questions (like my graphic)? ... or more complex, involving the use of this to then allow you to find something else?
There should be a list of ‘not-directly-trig geometry theorems’ ;-)
November 1, 2025 at 7:19 PM
There should be a list of ‘not-directly-trig geometry theorems’ ;-)
Yeah, you either know it or you don’t. It’s Elements VI – 3. The proof is rather pleasing.
mathcs.clarku.edu/~djoyce/java...
mathcs.clarku.edu/~djoyce/java...
Euclid's Elements, Book VI, Proposition 3
mathcs.clarku.edu
November 1, 2025 at 6:56 PM
Yeah, you either know it or you don’t. It’s Elements VI – 3. The proof is rather pleasing.
mathcs.clarku.edu/~djoyce/java...
mathcs.clarku.edu/~djoyce/java...
Ah, so that's what people call it ... makes sense. It's Proposition 3 of Book 6 of the Elements. It's not in the Scottish Secondary curriculum, sadly.
November 1, 2025 at 6:07 PM
Ah, so that's what people call it ... makes sense. It's Proposition 3 of Book 6 of the Elements. It's not in the Scottish Secondary curriculum, sadly.