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]]>I like the idea of establishing the interactive environment in the first talk for a class, though I’d think at a research conference it’s assumed by default that questions are welcome, particularly at the end of a talk. I remember Chelsea, who was the first plenary speaker at the AWM meeting, going out of her way to encourage questions at the start, but it didn’t seem to make too much of a difference.

I’m not sure my encouragement is going to do much either, of course. I guess my hope is more that there is some young woman out there who is just getting started in math, who reads my post and realizes that working past her own shyness might help her progress in a competitive field. It may make the difference for a few shy people here and there to just give some encouragement. I totally agree that it’s not going to solve any big systemic issue though.

]]>Perhaps it would be an interesting experiment, to ask a few people in advance, to prepare questions for the first talk (to ask both during and after) to set a good example.

Finally, a women-only venue is maybe a bit more prone to question-shyness, as in my personal experience, and some studies (see reference below) indicate that women are better at presenting ideas in a clearer fashion. Hence, there might not be any questions needed during a talk if it is easy to follow.

Diane F. Halpern, Camilla P. Benbow, David C. Geary,

Ruben C. Gur, Janet Shibley Hyde, and Morton Ann

Gernsbacher. The science of sex differences in science and

mathematics. Psychological Science in the Public Interest,

8(1):1–51, aug 2007

Odd perfect numbers, FLT,etc.

]]>Excuse my notation; I don’t know how to do your nice Latex reps.

a^2+b^2+c^2 = ab + bc + ca, iff the same is true for a’, b’ and c’ with:

a’=exp(i al) (a-zo); b’ = exp(i al) (b-zo); c’ = exp(i al) (c-zo)

Like you explain earlier, the later is just a translation a, b and c by an amount zo and then a rotation about the origin of al. This translation and rotation can be done to make number a lie on the x-axis and because its an equilateral triangle, numbers b and c be equal to number a rotated through 120 degrees in the plus and minus direction, respectively.

[Let zo be the centroid of a, b and c: zo = (a+b+c)/3; and al = -arg(a-zo).]

Then, original problem on equilateral triangles is equivalent to:

a^2+b^2+c^2 = ab + bc + ca iff zo and al can be found such that

a’, b’= a’ exp(i 2pi/3), c’ = a’ exp(-i 2pi/3) (this is the general equilateral triangle with centroid at the origin and number a on the x-axis)

For this choice of a’, b’ and c’:

a’ ^2 +b’^2 +c’^2 = a’b’ + b’ c’ +c’ a’ = a’^2 [1+exp(+i 2 pi/3) + exp(-i 2 pi/3)] ]]>

Parentheses

Logs/Exponents (left to right)

Mult/Div (left to right)

Add/Subtract (left to right)

Roots can be expressed as exponents; the log is the inverse of the exponent, as mult/div are inverses and add/subtraction are inverses.

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