POLYGONAL NUMBERS
\pˌɒlˈɪɡənə͡l nˈʌmbəz], \pˌɒlˈɪɡənəl nˈʌmbəz], \p_ˌɒ_l_ˈɪ_ɡ_ə_n_əl n_ˈʌ_m_b_ə_z]\
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If an arithmetical series whose first term is unity be written down, and the sum of the first two, first three, first four, etc., terms be taken, these sums are a series of P. N. ; the order being two more than the common difference of the arithmetic series. Thus, if the series is 1, 5, 9, 13, 17, etc., the corresponding polygonal numbers are 6, 15, 28, 45, etc. ; and as the common difference of the arithmetical series is 4, the P. N. are, in this case, hexagonal (4 + 2 = 6).
By Henry Percy Smith