Quantum redactiones paginae "Numerus triangularis" differant
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'''Numerus triangularis''' seu '''Numerus trigonalis'''<ref>[http://books.google.de/books?id=8LAY0Wjz7HoC&pg=PA89&lpg=PA89&dq=triangulum+harmonicum&source=bl&ots=GPNUPtJWWI&sig=TUmVldhH1_UYlVm9_h1fbAKO71A&hl=de&ei=Sfw3TcejLYiW8QOY3PXnCA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBsQ6AEwAQ#v=onepage&q=triangulum%20harmonicum&f=false Analysis 1 Von Wolfgang Walter] {{ling|Germanice}} |
'''Numerus triangularis''' <ref>[http://books.google.de/books?id=Hqw44qILcMoC&pg=PA191&lpg=PA191&dq=numeri+triangulares&source=bl&ots=rbUk-20ME4&sig=H9GTws1MPIQI-Yr8XRK8TKvJgqo&hl=de&ei=JEg5TbyHKoPFswbTw9XzBg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDsQ6AEwBQ#v=onepage&q=numeri%20triangulares&f=false Sämtliche Schriften und Briefe, Band 3 Von Gottfried Wilhelm Leibniz] [[Godefridus Guilielmus Leibnitius]] de numeribus triangularibus.</ref> seu '''Numerus trigonalis'''<ref>[http://books.google.de/books?id=8LAY0Wjz7HoC&pg=PA89&lpg=PA89&dq=triangulum+harmonicum&source=bl&ots=GPNUPtJWWI&sig=TUmVldhH1_UYlVm9_h1fbAKO71A&hl=de&ei=Sfw3TcejLYiW8QOY3PXnCA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBsQ6AEwAQ#v=onepage&q=triangulum%20harmonicum&f=false Analysis 1 Von Wolfgang Walter] {{ling|Germanice}} |
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</ref> est [[numerus naturalis]] qui a punctis in [[triangulum|triangulo]] positis fieri potest. Omnes scribi possunt quasi summa 1 + 2 + 3 + ... + '''''n''''', ubi '''''n''''' est numerus quiquam naturalis. Ergo, primi numeri triangularii sunt '' = 1, 2, 3...'' est |
</ref> est [[numerus naturalis]] qui a punctis in [[triangulum|triangulo]] positis fieri potest. Omnes scribi possunt quasi summa 1 + 2 + 3 + ... + '''''n''''', ubi '''''n''''' est numerus quiquam naturalis. Ergo, primi numeri triangularii sunt '' = 1, 2, 3...'' est |
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:[[I|1]], [[III|3]], [[VI|6]], [[X|10]], [[XV|15]], [[XXI|21]], [[XXVIII|28]], [[XXXVI|36]], [[XVL|45]], [[LV|55]], ... |
:[[I|1]], [[III|3]], [[VI|6]], [[X|10]], [[XV|15]], [[XXI|21]], [[XXVIII|28]], [[XXXVI|36]], [[XVL|45]], [[LV|55]], ... |
Emendatio ex 08:51, 21 Ianuarii 2011
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Numerus triangularis [1] seu Numerus trigonalis[2] est numerus naturalis qui a punctis in triangulo positis fieri potest. Omnes scribi possunt quasi summa 1 + 2 + 3 + ... + n, ubi n est numerus quiquam naturalis. Ergo, primi numeri triangularii sunt = 1, 2, 3... est
Cum omnis series sit longior uno puncto quam prior, perfacile visu ntum numerum triangularium esse summam primorum n numerorum naturalium.
Ut inveniatur ntus numerus triangularis, hac formula utere:
Aut quasi summa:
Proprietates
Una proprietas iucunda est: 2 numeri triangulares consequentes additi numerum quadratum aequant. E.g., 1 + 3 = 4 = 2^2, 3 + 6 = 9 = 3^3, 6 + 10 = 16 = 4^2, 10 + 15 = 25 = 5^2, etc. Hoc monstretur mathematico modo:
Vel graphico:
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Quadrati facti duobus numeris triangularibus consequentibus aduinctis.
Vide etiam
- Numerus tetrahedronalis - 3-D versio numeri triangularis.
- Numerus quadratus
- 666 - Numerus triangularis notissimus.
Nota
- ↑ Sämtliche Schriften und Briefe, Band 3 Von Gottfried Wilhelm Leibniz Godefridus Guilielmus Leibnitius de numeribus triangularibus.
- ↑ Analysis 1 Von Wolfgang Walter (Germanice)