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.
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?
Trying to write a question that requires the use of the Angle Bisector Theorem (Eu. El. VI – 3) … but failing … somehow a non VI – 3 solution always presents itself. Still, ended up with a nice enough question.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
November 3, 2025 at 1:08 PM
Trying to write a question that requires the use of the Angle Bisector Theorem (Eu. El. VI – 3) … but failing … somehow a non VI – 3 solution always presents itself. Still, ended up with a nice enough question.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
Does anyone teach this? Wondering if it's generally known or generally not known.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
November 1, 2025 at 5:38 PM
Does anyone teach this? Wondering if it's generally known or generally not known.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
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 :-)
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).
An hour in the wind this afternoon collecting an oak forest :-)
October 25, 2025 at 5:42 PM
An hour in the wind this afternoon collecting an oak forest :-)
Nice. With fractions I think of the denominator as a noun.
October 20, 2025 at 7:33 PM
Nice. With fractions I think of the denominator as a noun.
Been thinking more about the merits of the Exterior Angle Theorem and the fluency of pupils' geometric thinking. Here's a proof of one of @karencampe.bsky.social 's angle–arc theorems. Step 4 is beautifully immediate _if_ one uses Exterior-Angle-Theorem thinking.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
October 20, 2025 at 5:24 PM
Been thinking more about the merits of the Exterior Angle Theorem and the fluency of pupils' geometric thinking. Here's a proof of one of @karencampe.bsky.social 's angle–arc theorems. Step 4 is beautifully immediate _if_ one uses Exterior-Angle-Theorem thinking.
#UKMathsChat #iTeachMaths
#UKMathsChat #iTeachMaths
Zeta CfE Third Level.
October 13, 2025 at 5:53 PM
Zeta CfE Third Level.
Left: Requires triangle-interior-angle-sum and straight-angle-sum. 3 steps. Slower?
Right: Exterior Angle Theorem (Euclid 1–32). Requires corresponding and alternate angles. 1 step. Faster?
Right feels cleaner to me ... I wonder what pupils would think?
#UKMathsChat #iTeachMaths
Right: Exterior Angle Theorem (Euclid 1–32). Requires corresponding and alternate angles. 1 step. Faster?
Right feels cleaner to me ... I wonder what pupils would think?
#UKMathsChat #iTeachMaths
October 13, 2025 at 1:47 PM
Left: Requires triangle-interior-angle-sum and straight-angle-sum. 3 steps. Slower?
Right: Exterior Angle Theorem (Euclid 1–32). Requires corresponding and alternate angles. 1 step. Faster?
Right feels cleaner to me ... I wonder what pupils would think?
#UKMathsChat #iTeachMaths
Right: Exterior Angle Theorem (Euclid 1–32). Requires corresponding and alternate angles. 1 step. Faster?
Right feels cleaner to me ... I wonder what pupils would think?
#UKMathsChat #iTeachMaths
This one is a little harder to see because the vertex of the 55° angle coincides with the end of the 110° arc. But the 110° arc is still being subtended from a point on the circumference, so Eu III-20 still applies.
6/6
6/6
October 9, 2025 at 11:37 AM
This one is a little harder to see because the vertex of the 55° angle coincides with the end of the 110° arc. But the 110° arc is still being subtended from a point on the circumference, so Eu III-20 still applies.
6/6
6/6
... and the same again, this time starting at the 40°
1 → 2: Eu. III, 20
2 → 3: Supplementary arc.
3 → 4: Eu. III, 20
5/6
1 → 2: Eu. III, 20
2 → 3: Supplementary arc.
3 → 4: Eu. III, 20
5/6
October 9, 2025 at 11:37 AM
... and the same again, this time starting at the 40°
1 → 2: Eu. III, 20
2 → 3: Supplementary arc.
3 → 4: Eu. III, 20
5/6
1 → 2: Eu. III, 20
2 → 3: Supplementary arc.
3 → 4: Eu. III, 20
5/6
Start at the 20° and follow the sequence of steps.
1 → 2: Eu. III-20
2 → 3: Supplementary arc.
3 → 4: Eu. III-20
4/6
1 → 2: Eu. III-20
2 → 3: Supplementary arc.
3 → 4: Eu. III-20
4/6
October 9, 2025 at 11:37 AM
Start at the 20° and follow the sequence of steps.
1 → 2: Eu. III-20
2 → 3: Supplementary arc.
3 → 4: Eu. III-20
4/6
1 → 2: Eu. III-20
2 → 3: Supplementary arc.
3 → 4: Eu. III-20
4/6
Euclid's Elements Book 3 Proposition 20 (called by some the 'Inscribed Angle Theorem') will look like this: the arc is double the angle (on the circumference) that subtends it.
3/6
3/6
October 9, 2025 at 11:37 AM
Euclid's Elements Book 3 Proposition 20 (called by some the 'Inscribed Angle Theorem') will look like this: the arc is double the angle (on the circumference) that subtends it.
3/6
3/6
An arc of 30° will have a supplementary arc of 150°.
2/6
2/6
October 9, 2025 at 11:37 AM
An arc of 30° will have a supplementary arc of 150°.
2/6
2/6
A very short primer on mixing degrees of arc with degrees of angle for circle theorems.
#UKMathsChat #iTeachMath
Historically degrees measured arcs and arcs measured angles. This might feel uncomfortable but remember how we measure an angle today … with a protractor … measuring around an arc.
1/6
#UKMathsChat #iTeachMath
Historically degrees measured arcs and arcs measured angles. This might feel uncomfortable but remember how we measure an angle today … with a protractor … measuring around an arc.
1/6
October 9, 2025 at 11:37 AM
A very short primer on mixing degrees of arc with degrees of angle for circle theorems.
#UKMathsChat #iTeachMath
Historically degrees measured arcs and arcs measured angles. This might feel uncomfortable but remember how we measure an angle today … with a protractor … measuring around an arc.
1/6
#UKMathsChat #iTeachMath
Historically degrees measured arcs and arcs measured angles. This might feel uncomfortable but remember how we measure an angle today … with a protractor … measuring around an arc.
1/6
Yes, exactly. But try to avoid converting it back to what you know and work on the circumference rather than at the centre; all you really need to know is Euclid III, 21.
October 8, 2025 at 7:41 PM
Yes, exactly. But try to avoid converting it back to what you know and work on the circumference rather than at the centre; all you really need to know is Euclid III, 21.
Something I didn't know.
#UKMathsChat
#UKMathsChat
August 29, 2025 at 8:05 AM
Something I didn't know.
#UKMathsChat
#UKMathsChat
June 29, 2025 at 8:55 AM
Euclid. Elements. 1.47. I see what you mean!
June 14, 2025 at 5:15 PM
Euclid. Elements. 1.47. I see what you mean!
... just realised ... the orientation does have the merit of leading nicely to the basis of the Sine Rule ... i.e. a similar orientation.
June 14, 2025 at 10:42 AM
... just realised ... the orientation does have the merit of leading nicely to the basis of the Sine Rule ... i.e. a similar orientation.