## Wednesday, 27 February 2013

### WEDNESDAY, 27 FEBRUARY 2013

Today is the $58^{th}$ day of the year.

$58 = 2 \times 29$

$58 = 3^2 + 7 ^2$

$58 = 13 + 14 + 15 + 16$ which makes it a trapezoidal number, see here.

$58 = 2 + 3 + 5 + 7 + 11 + 13 + 17$ which means it is the sum of the first $7$ primes, see here.

$58$ is a hendecagonal number.  A hendecagonal number is the equivalent of a triangular number but for a shape that has 11 sides. The first 11 of the 11-gonal or hendecagonal numbers is as follows:
$0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415$

This series can also be generated by writing the natural numbers in a triangular spiral and then reading off the line that starts 0, 1, 11,

..................36
................37..35
..............38..15..34
............39..16..14..33
..........40..17.. 3..13..32
........41..18.. 4.. 2..12..31
......42..19.. 5.. 0.. 1..11..30..58
....43..20.. 6.. 7.. 8.. 9..10..29..57
..44..21..22..23..24..25..26..27..28..56
45..46..47..48..49..50..51..52..53..54..55