Dicuil (9th century) on triangular and square numbers
نویسندگان
چکیده
منابع مشابه
On the Square Roots of Triangular Numbers
1. BALANCING NUMBERS We call an Integer n e Z a balancing number if 1+ 2+ --+ (»l ) = (w + l) + (w + 2) +••• + (» + >•) (1) for some r e Z. Here r is called the balancer corresponding to the balancing number n. For example, 6, 35, and 204 are balancing numbers with balancers 2, 14, and 84, respectively. It follows from (1) that, if n is a balancing number with balancer r, then n2^(n + r)(n + r ...
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A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.
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ژورنال
عنوان ژورنال: British Journal for the History of Mathematics
سال: 2019
ISSN: 2637-5451,2637-5494
DOI: 10.1080/26375451.2019.1598687