Displaying similar documents to “On propellers from triangles.”

Polygonal Numbers

Adam Grabowski (2013)

Formalized Mathematics

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In the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = Δ+Δ+Δ”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar language evolved and attributes with arguments were implemented, we decided to extend these lines and...

A generalization of Pascal’s triangle using powers of base numbers

Gábor Kallós (2006)

Annales mathématiques Blaise Pascal

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In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.

Routh’s, Menelaus’ and Generalized Ceva’s Theorems

Boris A. Shminke (2012)

Formalized Mathematics

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The goal of this article is to formalize Ceva’s theorem that is in the [8] on the web. Alongside with it formalizations of Routh’s, Menelaus’ and generalized form of Ceva’s theorem itself are provided.