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Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". [2] In historical works about Greek mathematics the preferred term used to be figured number. [3] [4] In a use going back to Jacob Bernoulli's Ars Conjectandi, [1] the term figurate number is used for triangular numbers made up of ...
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number , other examples being square numbers and cube numbers . The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...
The triangular number sequence is the representation of the numbers in the form of equilateral triangle arranged in a series or sequence. These numbers are in a sequence of 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on.
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...
A triangular-pyramid version of the cannonball problem, which is to yield a perfect square from the N th Tetrahedral number, would have N = 48. That means that the (24 × 2 = ) 48th tetrahedral number equals to (70 2 × 2 2 = 140 2 = ) 19600. This is comparable with the 24th square pyramid having a total of 70 2 cannonballs. [5]
2 Figurate numbers. 3 Types of primes. 4 Base-dependent. 5 References. 6 External links. ... is the sum of the first n triangular numbers, with T(0) = 0 (empty sum ...
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The list above includes the perfect numbers 28 and 496. All even perfect numbers are triangular numbers whose index is an odd Mersenne prime. [2] Since every Mersenne prime greater than 3 is congruent to 1 modulo 3, it follows that every even perfect number greater than 6 is a centered nonagonal number.