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’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.
I thought your very beautiful solution deserved to be drawn :-)
October 27, 2025 at 8:26 PM
I thought your very beautiful solution deserved to be drawn :-)
Ah I see now! … that’s nice, very nice!!
October 26, 2025 at 8:31 PM
Ah I see now! … that’s nice, very nice!!
But you have the same red line issue that I have … how do you know it goes through the vertex of the large square?
October 26, 2025 at 7:08 PM
But you have the same red line issue that I have … how do you know it goes through the vertex of the large square?
I'm stuck too. Going round in circles ... struggling to prove that the red line goes through the red dot (which would lead on to a = b = 22½).
October 26, 2025 at 12:26 PM
I'm stuck too. Going round in circles ... struggling to prove that the red line goes through the red dot (which would lead on to a = b = 22½).
Definitely a Euler-ian ;-)
October 26, 2025 at 12:07 PM
Definitely a Euler-ian ;-)
Lol … remember my specialism, no? … trig 2CE – 12 CE … do you really want me to go there? ;-)
(Trig as ratios is broadly speaking from Euler 1748 … well, certainly Klügel 1770).
(Trig as ratios is broadly speaking from Euler 1748 … well, certainly Klügel 1770).
October 26, 2025 at 12:04 PM
Lol … remember my specialism, no? … trig 2CE – 12 CE … do you really want me to go there? ;-)
(Trig as ratios is broadly speaking from Euler 1748 … well, certainly Klügel 1770).
(Trig as ratios is broadly speaking from Euler 1748 … well, certainly Klügel 1770).