Bloggy young nerd women

Read the linked post from Michelle G. ” Picture yourself as a stereotypical male, about the question of intelligence, gender, and stereotype threat.”
The psychological investigations described were a real eye-opener to me. It is particularly relevant to MATH

mathbabe

Today I want to share with you all two recent blog posts from nerdy young women. And who doesn’t love nerdy young women!?

The first is by Michelle G, an M.I.T. student, class of 2018, who is majoring in “14,” which is M.I.T. code for economics. She wrote a blogpost called Picture yourself as a stereotypical male, about the question of intelligence, gender, and stereotype threat. I thought I knew all about that stuff but I learned quite a bit from her post. p.s. Larry Summers, I hope you read this.

The second is by Meena Boppana, a Harvard math major who has guest blogged here on mathbabe before. This post is called The Making of A Girl Mathlete, and it describes her experience winning math competitions, often as the only girl. Even though I personally think math contests kind of suck, I appreciate how much Meena…

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Halving a triangle, follow-up number three, bisecting an angle

While looking at the bisection of area formula (see previous posts)
a’b’ = (1/2)ab
where a’ and b’ are the distances from the vertex of points on the sides of the triangle, and a and b are the lengths of the sides I remembered another formula about triangles, the bisection of the angle formula, with a” and b” being the lengths of the two parts into which the opposite side is divided, namely
a”/b” = a/b

These are like Cuba and Puerto Rico, “Two wings of the same bird”, Jose Marti (in Spanish)
Neither involves the angle itself, and so is very general. I decided that there must be a connection, and after a futile look for some duality in the situation I suddenly saw the connection, in simple algebraic terms:
a’b’ = a’/(1/b’)
and so a triangle with sides a’ and 1/b’ will give a”/b” = a’b’
and then a”/b” = (1/2)ab as well.

This is the construction for the halving a triangle.

This is the extended construction for the bisector. The opposite side is in brown.

and this is a gif showing how as the point a’ (E) is moved the brown line (OE, opposite side) moves parallel to itself, thus preserving the value of the ratio a”/b”

And in case you got this far, some light relief. Bullfrog eats dog food, this morning. The dish is 10 inches across.