Browse by Topic

# Date Archive: 2018 April

## A Tale of Three Cosines—An Experimental Mathematics Adventure

Identifying Peaks in Distributions of Zeros and Extrema of Almost-Periodic Functions: Inspired by Answering a MathOverflow Question

One of the Holy Grails of mathematics is the Riemann zeta function, especially its zeros. One representation of is the infinite sum . In the last few years, the interest in partial sums of such infinite sums and their zeros has grown. A single cosine or sine function is periodic, and the distribution of its zeros is straightforward to describe. A sum of two cosine functions can be written as a product of two cosines, . Similarly, a sum of two sine functions can be written as a product of . This reduces the zero-finding of a sum of two cosines or sines to the case of a single one. A sum of three cosine or sine functions, , is already much more interesting.

Fifteen years ago, in the notes to chapter 4 of Stephen Wolfram’s A New Kind of Science, a log plot of the distribution of the zero distances... ... of the zero distribution of ---showing characteristic peaks---was shown.
Announcements & Events

## Five Ways to Make Your Technical Presentations Awesome

"Tell me and I forget. Teach me and I remember. Involve me and I learn." -- Benjamin Franklin I can count on one hand the best presentations I have ever experienced, the most recent being my university dynamics lecturer bringing out his electric guitar at the end of term to demonstrate sound waves; a pharmaceutical CEO giving an impassioned after-dinner oration about how his love of music influenced his business decisions; and last but not least, my award-winning attempt at explaining quantum entanglement using a marble run and a cardboard box (I won a bottle of wine). It's perhaps equally easy to recall all the worst presentations I've experienced as well---for example, too many PowerPoint presentations crammed full of more bullet points than a shooting target; infinitesimally small text that only Superman's telescopic vision could handle; presenters intent on slowly reading every word that they've squeezed onto a screen and thoroughly missing the point of a presentation: that of succinctly communicating interesting ideas to an audience.
Announcements & Events

## Introducing the Ultimate Technical Presentation Environment with Live Interactivity

We are delighted to announce that Wolfram's latest comprehensive notebook technology extension is here. Released with Version 11.3 of Wolfram desktop products, Wolfram Presenter Tools is the world's first fully computational presentation environment, seamlessly extending the notebook workflow for easy creation and delivery of dynamic presentations and slide shows, automatically scaled to fit any screen size. Our unique presentation features include rapid stylesheet updating and automatic slide breaking based on cell style.