Septenary
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| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil |
Burmese Khmer Lao Mongolian Thai |
| East Asian numerals | |
| Chinese Japanese Suzhou |
Korean Vietnamese Counting rods |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek Georgian Hebrew |
| Other systems | |
| Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit |
Kharosthi Mayan Quipu Roman Sumerian Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 24, 30, 36, 60, 64 | |
| Balanced ternary | |
| Non-positional system | |
| Unary numeral system (Base 1) | |
| List of numeral systems | |
The septenary numeral system is the base-7 number system, and uses the digits 0-6.
Contents |
[edit] Multiplication table
| 1 | 2 | 3 | 4 | 5 | 6 | 10 |
|---|---|---|---|---|---|---|
| 2 | 4 | 6 | 11 | 13 | 15 | 20 |
| 3 | 6 | 12 | 15 | 21 | 24 | 30 |
| 4 | 11 | 15 | 22 | 26 | 33 | 40 |
| 5 | 13 | 21 | 26 | 34 | 42 | 50 |
| 6 | 15 | 24 | 33 | 42 | 51 | 60 |
| 10 | 20 | 30 | 40 | 50 | 60 | 100 |
[edit] Fractions
Fractions expressed in septenary will repeat a sequence of digits unless the denominator is a power of seven. Few fractions can be expressed in a finite number of digits:
| Decimal | Septimal (periodic part) |
| 1/2 | 1/2 = 0.3... |
| 1/3 | 1/3 = 0.2... |
| 1/4 | 1/4 = 0.15... |
| 1/5 | 1/5 = 0.1254... |
| 1/6 | 1/6 = 0.1... |
| 1/7 | 1/10 = 0.1 |
| 1/8 | 1/11 = 0.06... |
| 1/9 | 1/12 = 0.053... |
| 1/10 | 1/13 = 0.0462... |
| 1/12 | 1/15 = 0.04... |
| 1/14 | 1/20 = 0.03... |
| 1/15 | 1/21 = 0.0316... |
| 1/16 | 1/22 = 0.03... |
| 1/18 | 1/24 = 0.025... |
| 1/19 | 1/25 = 0.024... |
| 1/20 | 1/26 = 0.0231... |
| 1/21 | 1/30 = 0.02... |
| 1/24 | 1/33 = 0.02... |
| ... | ... |
| 1/49 | 1/100 = 0.01 |
[edit] Irrational Numbers
| Algebraic irrational number | In decimal | In septenary | |
|---|---|---|---|
| √2 | (the length of the diagonal of a unit square) | 1.41421356237309... (≈ 1.414) | 1.262034545211232611 ... (≈ 1.262) |
| √3 | (the length of the diagonal of a unit cube, or twice the height of an equilateral triangle of unit side) | 1.73205080756887... (≈ 1.732) | 1.506044021410166456 ... (≈ 1.506 ≈ 1.5) |
| √5 | (the length of the diagonal of a 1×2 rectangle) | 2.2360679774997... (≈ 2.236) | 2.143654106250351 ... (≈ 2.144) |
| φ | (phi, the golden ratio = (1+√5)⁄2) | 1.6180339887498... (≈ 1.618) | 1.42166203646016... (≈ 1.422) |
| Transcendental irrational number | In decimal | In septenary | |
| π | (pi, the ratio of circumference to diameter) | 3.1415926535898... (≈ 3.1416) | 3.06636514320361341... (≈ 3.1) |
| e | (the base of the natural logarithm) | 2.718281828459045... (≈ 2.718) | 2.50124106542265... (≈ 2.5) |
One feature of this system is that 3.1 (= 22/7) approximates π with a relative error of 0.04 %.
[edit] In fiction
- The Tau of Sci-fi Table-top battle game Warhammer 40,000 use a base-7 counting system.
- In the New Series Adventures of Doctor Who, the time lords employ a number system using base 7.
- The Halo 3 Alternate Reality Game "IRIS" used a countdown clock in base-7.
- In the Halo videogame series, the Forerunners use a base-7 number system.
- In the online RPG Kingdom of Loathing, the Dwarven miners use a base-7 number system.
