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A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The -th triangle number is the number of dots in a triangle with dots on a side. A triangle number is, equivalently, the sum of the natural numbers from 1 to . The sequence of triangular numbers (sequence A000217 in OEIS) for is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ....

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  • Triangular number
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  • A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The -th triangle number is the number of dots in a triangle with dots on a side. A triangle number is, equivalently, the sum of the natural numbers from 1 to . The sequence of triangular numbers (sequence A000217 in OEIS) for is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ....
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abstract
  • A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The -th triangle number is the number of dots in a triangle with dots on a side. A triangle number is, equivalently, the sum of the natural numbers from 1 to . As shown in the rightmost term of this formula, every triangular number is a binomial coefficient: the -th triangular is the number of distinct pairs to be selected from objects. In this form it solves the "handshake problem" of counting the number of handshakes if each person in a room full of total people shakes hands once with each other person. The sequence of triangular numbers (sequence A000217 in OEIS) for is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ....
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