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Can someone please explain 'the director circle' (1 Viewer)

edd91

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Our maths teacher says he doesnt know it, so he wouldnt be confident teaching it, so can someone here explain it
 
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Why, yes, I can. The directror circle is a club which one can join, involving the Japanese American National Museum.

Exclusive benefits of Director's Circle Membership include:

- Invitations to exhibition opening receptions and other unique donor events throughout the year

- VIP tours of the National Museum

- Recognition in National Museum publications and on the Annual Giving Circles Wall (one-year)

- A special memento gift from the National Museum

- Plus all benefits of General Membership


Director's Circle agm-dir$1,000.00




serious response pending
 

edd91

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Originally posted by George W. Bush
Which conic are you intending to construct?
I am not sure how you construct a conic with it, it came up in fitzpatrick, 32(c), question 8, proving that tangents from a chord of contact lie at right angles, in the worked solutions, and we dunno what a director circle is
 
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the director circle is, i'm pretty sure, the two circles x^2+y^2=a^2 and x^2+y^2=b^2, which can be used to construct ellipses and hyperbolas.

(and circles too, I'd imagine;))
 

McLake

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Outside the scope of the syllabus (and none seems to know much about it *looks to spice girl, burchan or CM Tutor*)
 
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i think it's in the syllabus actually
i just don't think it's called the director circle

its quite tedious to explain, search on google
 

Affinity

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it's in one of cambridge or fitzpatrick under conics sketching
 

edd91

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it has the auxilery circle not the director circle
 

edd91

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Originally posted by buchanan
For an ellipse E: x<sup>2</sup>/a<sup>2</sup>+y<sup>2</sup>/b<sup>2</sup>=1, the director circle is C: x<sup>2</sup>+y<sup>2</sup>=a<sup>2</sup>+b<sup>2</sup> and it can be shown that if two tangents on E intersect on C, then they are perpendicular to each other.
Do you think it is ok to quote 'because they lie on the director circle' or does it need to be proven
 

edd91

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Sorry, thats what I meant, but once you prove their intersection lies on the director circle, is that enough to satisfy a marker?
 

edd91

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I actually do remember the third derivative thread and remember thinking it was kind of slack the markers cant recognise valid methods.
You would expect though that if a marker saw a method he didnt know, he'd ask senior markers??
 

maniacguy

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If it's an obscure result, it's reasonable for them to expect a student to prove it, I think. I mean, if not then basically every result with any sort of use would be given a name and markers would be wasting all of eternity looking up obscure results because someone thought "hey, that's just an application of #NAME#'s theorem".

It's like turtle's "well-known fact" result, it's just not practical.

Likewise, the arguement about the third derivative - it's certainly valid, but has the student learned how to use it or are they just taking something told to them on faith?

Whilst in practice a lot of the syllabus could just be taking things on faith, there is meant to be at least a veneer of encouraging understanding in there.

{Calling the third derivative result 'obscure' might be being a bit unfair, but it's not something the marker can be confident the student knows the reasoning behind. At least with the others, if the student uses it the marker can be fairly sure their teacher's tried to explain it to them}
 

KeypadSDM

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The third derivative method, however, is obscenely obvious. Also, many students who use the second derivative method, and dx either side might not know what they're doing, but they still get marked correctly.

The "not knowing reasoning behind" is a crap argument. Most people don't know what half of the memorised formulas they use mean.
 

turtle_2468

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So, how did you know that pi^2/6 < 7/4? Can you prove that without a calculator?

How about: sum of terms from 1/j^2 in the sequence < integral from (j-1) to infinity of x^(-2) dx (looking at the graph vs bar chart/Riemann sum of the terms)
= 1/j-1 upon solving.
Specifically letting j=3:
1/9+1/16+....< integral from 2 to infinity of x^(-2)=1/2
Hence sequence < 1+1/4+1/2=7/4.

I don't like the assumption of the meaning of "easy" above btw... proving the result + the 3 lines is much much harder than the proof above..
 

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