A series of blog posts of 100ish words for Mathober.

Internal

We usually think of a centre as being something internal. But not always.

Take a triangle. Suppose there’s a function, $f$, on the vertices, $a$, $b$ and $c$, for which $f(a, b, c)$ is the distance from $a$, $f(b, c, a)$ the distance from $b$ and $f(c, a, b)$ the distance from $c$. If a point exists that satisfies all three distances, then it’s a centre of the triangle. There are further conditions, but this is the basic idea.

Many of these centres are internal to the triangle, but many may also be external. So, for a triangle, a centre doesn’t have to be internal at all.

(101 words)

You can find out more about triangle centres at the Encyclopedia of Triangle Centers.