Nonperiodic tilings of the plane exhibit no translational symmetry. Penrose tilings are a remarkable class of nonperiodic tilings for which the set of prototiles consists of just two shapes. The pentagrid method, introduced by N.G. de Bruijn, allows us to generate Penrose tilings by taking a slice of the integer lattice in five-dimensional space. The empire problem asks: Given a subset of a Pen...

A 5-configuration is a collection of points and straight lines in the Euclidean plane so that each point lies on five lines and each line passes through five points. We describe how to construct the first known family of 5-configurations with chiral (that is, only rotational) symmetry, and prove that the construction works; in addition, the construction technique produces the smallest known geo...

the safavid dynasty was the first iranian centralized administration, which chose shia’a branch of islam as the official religion and the judicial system for iran. in safavi period the state officially established two separate and distinct court system. first the state courts (the urf courts) under the supervision of the secular minister of justice (divan-begi) and the secondly the islamic cour...

In that Empire, the Art of Cartography attained such Perfection that the map of a single Prov ince occupied the entirety of a City , and the map of the Empire, the entirety of a Prov ince. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Ge...

tiles and tilework has developed in islamic civilization based on pre-islamic iranian art and then spread out from spain to central asia. herein, iran has played an individual role among different islamic countries and remnants of various tileworks across this wide territory are clear evidences to this claim. among different species of tiles and tile decorations, we face with specific types of ...

Goldberg is a first-rate historian and it is good to have this 1989 volume on Prague Jewry in English, especially in Carol Cosman's literate and fluid translation. Goldberg surveys notions of illness, death, dying, and burial among the Jews of Prague from the sixteenth to the nineteenth centuries. Using communal records and ancillary sources, she provides detailed (and often extensive) quotatio...