… to continue slightly … I once saw a colleague create a circle question for an assessment but the circle he’d drawn wasn’t a circle, it was an ellipse … and he refused to change it! Would you be okay with that? (Maybe I am overly pedantic, I don’t know).
But in F the angle drawn at 55° is less than the angle drawn at 35°?? To me that’s a bit odd. I appreciate that drawing accurately with certain software is time consuming but (for me) things should look/feel about right.
I mean maybe yes. And geometry is my thing so I do like it right. And I was confused by it. So pedantic maybe but genuine yes.
I just wonder if in algebra people would be happy with, say:
‘Solve 7x + 4 = 4X +10’
?
Task 4 … again, it’s not to scale … that’s not a 53° angle. Why present something that is obviously incorrect/misleading/confusing?
Task 2 … I don’t understand the point of the triangles not being drawn to scale? Some are wildly off. I find it all a bit confusing. What am I missing?
lol. I second that.
Infinitesimals … but I rather liked Henle! … made a lot more sense to me than those funny limit things ;-)
a²/2 … by considering the two extreme cases ;-)
This?
How do we know the red line running from x to y intersects at P?
And how do we conclude all these things without knowing the answer is 45°?
Changed my mind ... I still don't understand it!
I get that the midpoint of the green/teal line will be on the small circle ... and at the West cardinal point of the small circle.
But I don't get why we know the red line running from x° to y° will also intersect at this same point.
This one (I hope) side-steps the 135°. I've scaled the lines in the small semi-circle by a factor or 2. The t° bit hopefully ensures the pink-double-arrow line intersects with the West cardinal point, thereby bounding the purple arc at 90°.
Ah, yes ... of course ... thank you :-)
Why does P lie on the small circle?
You’d need to work in sexagesimal for full authenticity ;-)
Made this last year ... wanted something that emphasised the area relationship without always having to work out a side length ... and I wanted to avoid algebra. I explain the relationship using the first sheet ... and the second sheet they pretty much just get on with. Doesn't last a whole lesson.
60 − 20 − 8 − 6 = 26
Ah yes ... so it is ... after a little rearranging. I'd never actually seen it in use before. Thank you!
Anyone know what this is called? Is it a thing?! Found it in Bīrūnī from the 11th century ... as one does.
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I meant that the two different approaches can make the problem seem to be about different things. Contrast Paddy MacMahon’s solution to the last Catriona Agg Puzzle and mine. His is a double application of Pythagoras. Mine is more about symmetry in a square. Makes the puzzle hard to categorise!
Not necessarily an easy task! I’m always struck by the split between those who throw algebra at the problem and those that stay within traditional geometry.
Great. Thanks so much for taking the time :-)
I remember thinking that establishing a culture of neriage could take … well, months rather than weeks with many classes … and I just didn’t have the energy for it at the time.
I’m thinking of buying a visualiser … either an IPEVO DO-CAM or an Innex DC500. If you use either of these I’d love to hear your views of them … particularly any shortcomings.
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Be interested to hear how you get on with the neriage part … I was never brave enough to fully embrace the spirit of it … but I love the idea of it.
There were no takers for this … but here's the solution for completeness. It's all similar triangles ... with some fancy ratio table moves; the reductions come from common diagonals in the upper pair … and common columns in the bottom pair. Classical moves that we're maybe less familiar with today.
I seem to be ever late to the Agg puzzle releases. The way I see it the symmetry of the overlapping red squares ensures the 4-small-squares area equals the yellow-square area. I like the way the purple square dictates the size of all the other squares.
An under-used approach I’ve always felt.