John D. Cook | Applied Mathematics Consulting

Pascal’s triangle is the most famous triangular arrangement of numbers. I’ve written about other numerical triangles, such as Bell’s triangle and the trinomial triangle. There’s another well-known triangle that somehow I never heard of until recently: the harmonic triangle, first explored by Leibniz around 1700. To create the harmonic triangle, start with the harmonic series […] The post Harmonic triangle first appeared on John D. Cook.

A few days ago I wrote about topological models of modal logic. If you find general topology more familiar than modal logic, this correspondence could be helpful. If you think the motivation for general topology is evident but the motivation for modal logic is suspect, the correspondence between the two fields might relieve some of […] The post Categorical models of logics first appeared on John D. Cook.

If you’ve followed this blog for a while, you may know that I do a lot of work with data privacy and that I have an interest in modal logic. Recently these two worlds collided: I became aware of work that uses modal logic to reason about data privacy. The story begins with Helen Nissenbaum’s […] The post Privacy policies and modal logic first appeared on John D. Cook.

The Riemann Hypothesis (RH) is the conjecture that all the zeros of the Riemann zeta function ζ(s) in the critical strip, i.e. the region of the complex plane with real part between 0 and 1, have real part equal to ½. The Quasi Riemann Hypothesis (QRH) says that there exists a constant θ < 1 […] The post Consequences of progress toward the Riemann Hypothesis first appeared on John D. Cook.

I was skimming through David Well’s book The Penguin Dictionary of Curious and Interesting Geometry and was surprised by this entry: Lissajous figures or Bowditch curves First discussed by Nathaniel Bowditch in 1815, and later by Jules Antoine Lissajous in 1857 … I wrote a couple posts about Lissajous curves years ago, and recently I wrote […] The post Lissajous and Bowditch first appeared on John D. Cook.