Tea Tasting and Pascal Triangles

Tasting Tea By SIR RONALD

TASTI: Tasting and Socializing Tabletop Interface

Tabletop displays are a growing area of research for studying social interactions. In this paper, we present TASTI (Tasting and Socializing Tabletop Interface), a novel interaction technique for enhancing tasting events, such as a wine-tasting. Users interact with TASTI’s digital display by manipulating physical objects (such as wine bottles) placed on the table. Each bottle’s position is track...

Rotational and dihedral symmetries in Steinhaus and Pascal binary triangles

We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.

A universal sequence of integers generating balanced Steinhaus figures modulo an odd number

In this paper, we partially solve an open problem, due to J. C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer n, that are Steinhaus triangles containing all the elements of Z/nZ with the same multiplicity. For every odd number n, we build an orbit in Z/nZ, by the linear cellular automaton generating the Pascal triangle modulo n, which contains infi...

Large primes in generalized Pascal triangles

In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 ...