Mathematical Numbers via ART

Mathematical Font Art

Currently, only a limited number of fonts are available for high quality mathematical typesetting, such as Knuth's computer modern font, the Stix font, and several fonts from the TEX Gyre family. An interesting challenge is to develop tools which allow users to pick any existing favorite font and to use it for writing mathematical texts. We will present progress on this problem as part of recen...

Bounding Helly Numbers via Betti Numbers

We show that very weak topological assumptions are enough to ensure the existence of a Hellytype theorem. More precisely, we show that for any non-negative integers b and d there exists an integer h(b, d) such that the following holds. If F is a finite family of subsets of R such that β̃i ( ⋂G) ≤ b for any G ( F and every 0 ≤ i ≤ dd/2e−1 then F has Helly number at most h(b, d). Here β̃i denotes t...

Neural correlates of numbers and mathematical terms

Numerical processing has been demonstrated to be subserved typically by the brain regions around the bilateral intraparietal sulcus (IPS). The goal of the current study was to investigate whether the processing of mathematical terms shared the same brain regions with numerical processing. Healthy adult participants performed semantic distance judgment tasks on five types of materials, including...

Developing Mathematical Tools to Investigate Art

It all started (at least for my students and myself) in December 2006, at a colloquium talk in Applied Mathematics at Princeton University, by Rick Johnson, a distinguished professor in Electrical Engineering at Cornell University, freshly back from a year’s sabbatical in the Netherlands. At the end of his talk, he advertised the possibility for some very interesting and challenging Image Proce...

Mathematical Fuzzy Logic { State of Art