An Introduction to Proofs and the Mathematical Vernacular

An Introduction to Proofs and the Mathematical Vernacular 1

Why Do Informal Proofs Conform to Formal Norms?

Kant discovered a philosophical problem with mathematical proof. Despite being a priori, its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathema...

Introducing a Lightweight Structural Model via Simulation of Vernacular “Pa Tu Pa” Arch

The knowledge of Iranian vernacular structures is based on geometry, and there is a possibility of recreating such structural patterns aimed at producing movable structures. The purpose of this research was to utilize the patterns of vernacular structures to provide a lightweight structural model. The questions raised included how to create various forms based on the structural history of any r...

Introduction to Schramm-Loewner evolution and its application to critical systems

In this short review we look at recent advances in Schramm-Loewner Evolution (SLE) theory and its application to critical phenomena. The application of SLE goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. Through the use of SLE, the evolution of conformally invariant paths on the complex plane can be followed; hence a...

Factors Affecting Vernacular Architecture in Nosmeh Village (Paveh County)

Vernacular architecture is among the most valuable phenomena, which has manifested cultural, historical, social, religious values and so on by itself. The values inherent to vernacular architecture of each city reflect the thinking of the people from that city. Therefore, the peace and quality of people's life can depend on preserving the same architectural values. Preserving and integrating of...