Mathematical art and artistic mathematics

ABSTRACT

The purpose of this note is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of geometry and algebra.     

Mathematical statistics and problems of ancient chronology. A new approach

New methods of processing statistically quantitative textual information of a narrative character are introduced. The methods can be used to recognize dependent and independent texts among large collections of texts. The methods are applied to the problem of correct dating of the events in ancient chronology. These results induce conjecture on the redating of some historical events.     

Two letters from Otto Neugebauer to Thomas Eric Peet on ancient Egyptian mathematics

We describe two letters of 1926 from the historian of mathematics Otto Neugebauer to the Egyptologist Thomas Eric Peet (Griffith Institute Archive, Oxford: Peet MSS 4.9). The letters concern Neugebauer's study of certain parts of the Rhind Mathematical Papyrus, as found in the doctoral dissertation that he had completed in Göttingen that year, for which Peet's 1923 edition of the papyrus was a major source. In the letters, we see the young Neugebauer establishing himself within the wider Egyptological community. The letters open up a discussion of Peet's own work on ancient Egyptian mathematics.     

Mathematical aspects of educating architecture designers: a college study

This paper considers a second-year Mathematical Aspects in Architectural Design course, which relies on a first-year mathematics course and offers mathematical learning as part of hands-on practice in architecture design studio. The 16-hour course consisted of seminar presentations of mathematics concepts, their application to covering the plane by regular shapes (tessellations), and an architecture design project. The course follow-up examined the features of mathematical learning in the studio environment using qualitative methods. It showed students’ curiosity and motivation to deepen in mathematical subjects and use them in their tessellation design projects. The majority of the students refreshed and practically applied their background mathematical knowledge, especially in calculus, on a need-to-know basis.     

Diagrams in ancient Egyptian geometry: Survey and assessment

This article surveys and catalogs the geometric diagrams that survive from ancient Egypt. These diagrams are often overspecified and some contain inaccuracies in their construction. The diagrams accompany algorithmic texts and support the mathematical programme of their authors. The study concludes with a brief comparison with the diagram traditions of ancient Babylon, early India, and Greece.     

On Tutt's Characterization of graphic matroids—a graphic proof

In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of ‘signed graph’ and it is ‘graphic’ in the sense that it can be presented almost entirely by drawing (signed) graphs. © 1995 John Wiley & Sons, Inc.     

Generalized splines and graphic arrangements

We define a chain complex for generalized splines on graphs, analogous to that introduced by Billera and refined by Schenck–Stillman for splines on polyhedral complexes. The hyperhomology of this chain complex yields bounds on the projective dimension of the ring of generalized splines. We apply this construction to the module of derivations of a graphic multi-arrangement, yielding homological criteria for bounding its projective dimension and determining freeness. As an application, we show that a graphic arrangement admits a free constant multiplicity if and only if it splits as a product of braid arrangements.     

Filters and simple graphic algebras

The latticeU(S) of the filters of a finite joinsemilattice S is considered and it is shown when the Hasse diagram graph of S generates a simple graphic algebra.