Number

18

18 — Chai, “life”

18 is a composite number, even, a calendar year.

In Hebrew, letters double as numerals, so words carry sums. חי — chet (8) plus yod (10) — spells chai, “life,” and totals 18. Eighteen is, quite literally, the number that spells living.

This is one of the rare cases where gematria steps out of mysticism and onto an actual cheque. Gifts at weddings, bar and bat mitzvahs, and donations to charity are given in multiples of 18: $18, $36 for “double chai,” $180, $1,800. The toast l'chaim — “to life” — invokes the same word. Ask why the amount is $36 rather than $35 and the answer is a two-letter Hebrew word.

Double chai does further duty of its own: tradition holds that every generation contains 36 righteous people — the lamed vav tzadikim — unknown even to themselves, on whose merit the world quietly continues. One last property, with no theology attached: 18 is the only positive integer that is exactly twice the sum of its own digits (1 + 8 = 9, and 9 × 2 = 18).

Sources https://en.wikipedia.org/wiki/Chai_(symbol) · https://en.wikipedia.org/wiki/Gematria

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Interestingness

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Historical context — 18 AD

Calendar year

AD 18 (XVIII) was a common year starting on Saturday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Historical context — 18 BC

Calendar year

Year 18 BC was either a common year starting on Friday, Saturday or Sunday or a leap year starting on Saturday of the Julian calendar and a common year starting on Thursday of the Proleptic Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Monday
January 1, 18
Ended on: Monday
December 31, 18
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 10s
10–19
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,008
2008 years before 2026.

In other calendars

Hebrew: 3778 / 3779 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Earth zodiac:Tiger
Sexagenary cycle position 15 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 561 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 10 / 11 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -60 / -61 Saka
Indian national calendar; year starts in March.

Cultural significance

Jewish lucky

Symbol of life; common gift amount at weddings and bar/bat mitzvahs.

Hebrew letters חי (chet + yod) spell "chai" ("life") and have a gematria value of 18.

Wikipedia ↗

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Even
Digit count: 2
Digit sum: 9
Digit product: 8
Digital root: 9
Palindrome: No
Bit width: 5 bits
Reversed: 81
Flips to (rotate 180°): 81
Recamán's sequence: a(23) = 18
Square (n²): 324
Cube (n³): 5,832
Divisor count: 6
σ(n) — sum of divisors: 39
φ(n) — Euler's totient: 6
Sum of prime factors: 8

Primality

Prime factorization: 2 × 3 ²

Nearest primes: 17 (−1) · 19 (+1)

Divisors & multiples

All divisors (6)

1 · 2 · 3 · 6 · 9 (half) · 18

Aliquot sum (sum of proper divisors): 21

Factor pairs (a × b = 18)

1 × 18

2 × 9

3 × 6

First multiples

18 · 36 (double) · 54 · 72 · 90 · 108 · 126 · 144 · 162 · 180

Sums & aliquot sequence

As a sum of two squares: 3² + 3²

As consecutive integers: 5 + 6 + 7 3 + 4 + 5 + 6

Aliquot sequence: 18 → 21 → 11 → 1 → 0 — terminates at zero

Continued fraction of √n

√18 = [4; (4, 8)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: eighteen
Ordinal: 18th
Roman numeral: XVIII
Binary: 10010
Octal: 22
Hexadecimal: 0x12
Base64: Eg==
One's complement: 237 (8-bit)
Scientific notation: 1.8 × 10¹

In other bases

ternary (3) 200

quaternary (4) 102

quinary (5) 33

senary (6) 30

septenary (7) 24

nonary (9) 20

undecimal (11) 17

duodecimal (12) 16

tridecimal (13) 15

tetradecimal (14) 14

pentadecimal (15) 13

As an angle

18°

18° ≈ 0.314 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ιηʹ
Mayan (base 20): 𝋲
Chinese: 一十八
Chinese (financial): 壹拾捌

In other modern scripts

Eastern Arabic ١٨ Devanagari १८ Bengali ১৮ Tamil ௧௮ Thai ๑๘ Tibetan ༡༨ Khmer ១៨ Lao ໑໘ Burmese ၁၈

Digit at this position in famous constants

π — Pi (π): Digit 18 = 3
e — Euler's number (e): Digit 18 = 3
φ — Golden ratio (φ): Digit 18 = 4
√2 — Pythagoras's (√2): Digit 18 = 4
ln 2 — Natural log of 2: Digit 18 = 0
γ — Euler-Mascheroni (γ): Digit 18 = 6

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 18, here are decompositions:

5 + 13 = 18
7 + 11 = 18

ASCII character

As an ASCII codepoint, 18 is control character (0x12). ASCII control character.

Hex color

#000012

RGB(0, 0, 18)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.18.

Address: 0.0.0.18
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.18

Unspecified address (0.0.0.0/8) — "this network" placeholder.

Musical pitch

Heard as a frequency, 18 Hz is closest to:

Concert pitch (A4 = 440 Hz): D0 (18.4 Hz, -34¢)
Scientific pitch (C4 = 256 Hz): D0 (18 Hz, +4¢)
Baroque pitch (A4 = 415 Hz): D♯0 (18.3 Hz, -32¢)

(below the ~20 Hz floor of human hearing — likely inaudible)

As a MIDI note number, 18 is F♯0 (23.1 Hz at concert pitch). (very low — many laptop and phone speakers can't reproduce it)

Atomic number

On the periodic table, atomic number 18 is Argon (Ar) — period 3.

Argon on Wikipedia ↗