John D. Cook • 4/1/2026

Pentagonal numbers are truncated triangular numbers

This article discusses the mathematical relationship between pentagonal numbers and triangular numbers, showing that pentagonal numbers are truncated triangular numbers. It provides a visual proof by warping the diagram of the nth pentagonal number into the base of the (2n-1)st triangular number, and also gives an algebraic proof using the formulas Pn = (3n² − n)/2 and Tn = (n² − n)/2. The content is focused on number theory and mathematical proofs, which falls under computer science and algorithms.

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#mathematics #number theory #Algebra