The “Nine-Point Circle” of a triangle \(\triangle ABC\) contains the vertices of the medial triangle (\(\triangle RST \)) and orthic triangle (\(\triangle UVW \)), as well as points \(X\), \(Y\), \(Z\) that bisect segments from \(\triangle ABC\)’s orthocenter (\(H\)) to its vertices. A question on Math.StackExchange.com asked for proof that the center of the nine-point circle […]
Archive for the ‘Misc. Math’ Category
A question at Math.StackExchange asked about “Ceva’s Theorem in three dimensions”. So I derived one. The result (which I believe may be new, although it could very well exist in the hundreds of years of mathematical literature since Ceva) replaces the traditional ratios of segment lengths with “triple-ratios” of triangle areas, to satisfying effect. Whereas […]
What’s the largest possible amount of money you can win in a single game of TV’s “Jeopardy!”? Read my note This … is … “Maximal Jeopardy!” to find out.
… for non-negative \(x\) and real \(n\), not both zero.