Mathematical Community

Today is the birthday of Pierre Brocard born 1845 Vignot, France.  He was best known for his discovery of the so-called Brocard points of a triangle.

In a triangle ABC with sides a, b, and c, where the vertices are labeled A, B and C in counterclockwise order, there is exactly one point P such that the line segments AP, BP, and CP form the same angle, ω, with the respective sides c, a, and b, namely that angle PAB = angle PBC = angle PCA.

Point P is called the first Brocard point of the triangle ABC, and the angle ω is called the Brocard angle of the triangle.  The Brocard point is constructed at the intersection of  3 circles.

I had mentioned previously that I was prodded by a colleague to start working on my master's degree in mathematics.  Another factor in my motivation was the regular mathematical dialogue between us while we commuted.  He was taking a class on problem solving and I had not yet began working on my degree.  As we commuted, he would pose a problem and we would generate solutions without paper, pencil, and most definitely without a calculator.  If our answers differed, we would justify our solutions with the mathematical knowledge we had at hand.  I found that our mathematical discourse to be gratifying.  I had to be part of a community where I could have those types of conversations so I began that educational journey.

I suppose the reason why people choose to form book clubs or musicians gather to jam is to share and learn.  The exchange of intellectual thought appears to be part of our genetic code.  A Greek Gymnasium was a place for socializing and engaging in intellectual pursuits.  After we satisfy our basic needs, we seek an intellectual community.

I often feel that mathematicians are viewed as isolationists but in reality mathematicians search for a community in which the enjoyment of mathematics can be shared.  I attended a presentation on the derivation of the cubic formula, a formula similar to the quadratic formula but used in cubic functions. In the middle of the presentation, I paused my attention and observed the audience.  The audience hung on every word.  The questions and discourse that followed was lively and excited.

At the state Math League Competition, hundreds of students were also filled with excitement and anticipation watching what is dubbed the Math Bowl, eight students on stage, answering mathematics questions within a 90 second time period sometimes not using a calculator.  They were part of a mathematical community where others like themselves were gathered doing math.