280 (number)#285
{{Hatnote|This article covers the number 280. For the year, see 280.}}
{{Refimprove|date=May 2016}}
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280 (two hundred [and] eighty) is the natural number after 279 and before 281.
In mathematics
The denominator of the eighth harmonic number,{{Cite web|url=https://oeis.org/A002805|title=Sloane's A002805 : Denominators of harmonic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}} 280 is an octagonal number.{{Cite web|url=https://oeis.org/A000567|title=Sloane's A000567 : Octagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}} 280 is the smallest octagonal number that is a half of another octagonal number.
There are 280 plane trees with ten nodes.
As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations). {{disputed-inline|reason=This seems to be an error, the number of plane (rooted) trees with ten vertices and the number of handshakes (non-intersecting chords with 18 points around a circle) should both be the ninth Catalan number. OEIS http://oeis.org/A000108 for the Catalan numbers has both of these ideas listed,
"Ways of joining 2n points on a circle to form n nonintersecting chords." so 18 points is ninth Catalan #
and "a(n) is the number of ordered rooted trees with n nodes, not including the root." so again, 10 roots is Catalan (9). And this number is 4862, not 280.|date=September 2013}}