Triangular numbers: Difference between revisions
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In general, these all belong to the class [[wp:Figurate_number|figurate numbers]] as they are |
In general, these all belong to the class [[wp:Figurate_number|figurate numbers]] as they are |
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based on '''r''' dimensional geometric figures. Sometimes they are referred to as '''r-simplex''' |
based on '''r''' dimensional geometric figures. Sometimes they are referred to as '''r-simplex''' |
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numbers. In geometry a [[wp:Simplex|simplex]] is the simplest '''r-dimensional''' |
numbers. In geometry a [[wp:Simplex|simplex]] is the simplest possible '''r-dimensional''' |
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object |
object. |
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You may easily extend to an arbitrary dimension '''r''' using binomials. Each term '''n''' in dimension '''r''' is <math>r_n = \binom{n + r - 1}{r}</math> |
You may easily extend to an arbitrary dimension '''r''' using binomials. Each term '''n''' in dimension '''r''' is <math>r_n = \binom{n + r - 1}{r}</math> |
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There is no known general formula to find |
There is no known general formula to find higher r-simplex roots. |
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