Dissection of Polygon into Triangles with Chords

Theorem

The number of different ways $k$ a convex $n$-sided polygon can be divided into triangles using chords, not counting reflections and rotations as different, is given for the first few $n$ as follows:

$n$	$k$
$3$	$1$
$4$	$1$
$5$	$1$
$6$	$3$
$7$	$4$
$8$	$12$
$9$	$27$
$10$	$82$
$11$	$228$
$12$	$733$
$13$	$2282$

This sequence is A000207 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

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Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $27$