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Just wondering how much we'll need to know for the mid-term, upto what unit, for instance? Occasionally the more complex equations have been called extraneous since algebra is not prerequisite. Will calculators be necessary/permitted?

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The last section we covered was about fractals. There was a handout given some time ago listing the sections in the book and describing how they correspond to the lectures. Calculators will not be permitted (nor needed) for the exams.

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will we need to know the Other Transformations of the plane for the midterm (such as the squaring transformation or the moebius) ?

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You do not need to memorize them. If they appear in the midterm, their definitions will be provided.

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dividing a line segment such that one part is twice longer than the other:

if we have a line seg AB and we divide it into 3 equal parts (denoting the cuts as C and D), we could then remove D, such that CB were now twice longer than AC: is this an acceptable way to do it or is erasing D a rule-breaker?

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No need to erase anything (if you do, then perhaps it would not be clear how you got your points). You would need to say that C is the point that divides the segment as needed.

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In the solutions for Midterm exam Feb 2006 (question 2b), the word "duplicating" is used to mean "doubling". I just want to be sure to avoid confusion: Duplicate means copy, not double, right?

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Yes, you are right. Slip. Should have been "doubling".

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on the october 16th 2003 midterm posted online part b of the first question asks to construct an equilateral triangle of angle B over a given base. The problem is that equilateral triangles have 3 angles of 60 degrees, while angle B is about 32 degrees. Is this a mistake? If so, what should the question read?

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do you know when the mid-term results will be posted?

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Sometime next week before the Thursday class.