Triangular Numbers and Running Expressions with Equalities

In previous work ( Part I, Part II, Part III), running equalities are written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. Each digits is used once with basic operations, along with factorial, square-root and Fibonacci sequence values. These types of equalities, we … Continue reading Triangular Numbers and Running Expressions with Equalities

Natural Numbers in Terms of Fibonacci and S-gonal Values

This paper brings natural numbers from 1 to 10000 in terms of Fibonacci and S-gonal numbers, in particular, Triangular and Squared values. In case of triangular and square numbers, some initial values are not available. While, in case of Fibonacci numbers, all the numbers are available. The work is divided in two parts: one from … Continue reading Natural Numbers in Terms of Fibonacci and S-gonal Values

Fibonacci Sequence and Running Expressions with Equalities

  In previous work ( Part I   and Part II), running qualities are written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. Each digits is used with basic operations, along with factorial and square-root. These types of equalities, we called as running expressions. … Continue reading Fibonacci Sequence and Running Expressions with Equalities

Fibonacci Sequence and Running Expressions with Equalities – I

In the previous works ( Parts I and II), running exprssions written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by one or more equality signs. Each digit appears once. Along with basic operations, factorial and square-root are also used. These types of expressions are understood as running expressions. … Continue reading Fibonacci Sequence and Running Expressions with Equalities – I