Quantum redactiones paginae "Numerus triangularis" differant
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==Proprietates== |
==Proprietates== |
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Una proprietas iucunda est: 2 numeri triangulares consecuquentes, cum sibi additi, [[numerus quadratus]] aequant. Ita, |
Una proprietas iucunda est: 2 numeri triangulares consecuquentes, cum sibi additi, [[numerus quadratus]] aequant. Ita, 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16, 10 + 15 = 25, etc.Hoc monstretur mathematico modo: |
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Vel graphico: |
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Alternatively, it can be demonstrated graphically, thus: |
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|[[Image:Square triangle sum 25.png]] |
|[[Image:Square triangle sum 25.png]] |
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Quadrati facti duobus numeris triangularibus consequentibus aduinctis. |
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In each of the above examples, a square is formed from two interlocking triangles. |
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More generally, the difference between the nth m[[-gonal number]] and the nth (m+1)-gonal number is the (n-1)th triangular number. For example, the sixth [[heptagonal number]] (81) minus the sixth [[hexagonal number]] (66) equals the fifth triangular number, 15. |
More generally, the difference between the nth m[[-gonal number]] and the nth (m+1)-gonal number is the (n-1)th triangular number. For example, the sixth [[heptagonal number]] (81) minus the sixth [[hexagonal number]] (66) equals the fifth triangular number, 15. |
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See [[Tetrahedral number]] for a three dimensional version of triangular numbers. Triangular numbers and tetrahedral numbers are just two of many types of [[figurate numbers]]. |
See [[Tetrahedral number]] for a three dimensional version of triangular numbers. Triangular numbers and tetrahedral numbers are just two of many types of [[figurate numbers]]. |
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==Vide etiam== |
==Vide etiam== |
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* [[Numerus tetrahedronalis]] - 3-D versio numeri triangularis. |
* [[Numerus tetrahedronalis]] - 3-D versio numeri triangularis. |
Emendatio ex 13:24, 30 Novembris 2006
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Numerus triangularis est numerus naturalis qui representetur a triangulo facto cum eodem numero punctorum. Omnes potest scribier quasi summa 1 + 2 + 3 + ... + n, cum n est numerus quiquam naturalis. Ergo, ordo numerorum triangularium pro ullo n = 1, 2, 3... est
Cum omnis series est longior uno quam priore, perfacile visu num numerum naturalem esse summam priorum n numerorum naturalium consequentum.
Ut invenias num numerum triangularem, hac formula utere:
Aut quasi summa:
Proprietates
Una proprietas iucunda est: 2 numeri triangulares consecuquentes, cum sibi additi, numerus quadratus aequant. Ita, 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16, 10 + 15 = 25, etc.Hoc monstretur mathematico modo:
Vel graphico:
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25 |
Quadrati facti duobus numeris triangularibus consequentibus aduinctis.
Vide etiam
- Numerus tetrahedronalis - 3-D versio numeri triangularis.
- Numerus quadratus
- 666 - Numerus triangularis gnotissimus.