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Triangle Numbers
by Daniel Pietrobon
Pages 2 and 3 of 7
Triangle
Numbers
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The
natural numbers
are given by 1, 2, 3, 4, 5, 6, ... etc.
Rounded Rectangle
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1
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2
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3
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4
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5
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6
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The
triangle numbers
are the sums of the first
n
natural numbers.
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The
triangle numbers T
n
are the sums of the first
n
natural numbers.
T
1
= 1
T
2
= 1 + 2
T
3
= 1 + 2 + 3
T
4
= 1 + 2 + 3 + 4
T
5
= 1 + 2 + 3 + 4 + 5
T
6
= 1 + 2 + 3 + 4 + 5 + 6
.
.
.
.
.
.
etc.
They are so named because they form a triangle of size n.
The
tetrahedral numbers
are the sums of the first
n
triangle numbers.
Challenge [hard]:
What comes next?
Attributions:
Page 5:
Pyramid of 35 spheres animation
Uploaded to Wikimedia Commons 1 August 2005 by User: Blotwell
CC BY-SA 3.0
Page 6:
Pascal triangle simplex numbers
Uploaded to Wikimedia Commons 12 April 2014 by User: Cmglee
CC BY-SA 4.0
