Tlalcuahuitl [t͡ɬaɬˈkʷawit͡ɬ] or land rod also known as a cuahuitl [ˈkʷawit͡ɬ] was an Aztec unit of measuring distance that was approximately 2.5 m (8.2 ft), 6 ft (1.8 m) to 8 ft (2.4 m) or 7.5 ft (2.3 m) long.
The abbreviation used for tlalcuahuitl is (T) and the unit square of a tlalcuahuitl is (T²).
|Glyph||English||Nahuatl||IPA||Fraction of Tlalcuahuitl||Metric Equivalent |
where 1 T = 2.5 m
|arrow||cemmitl||[ˈsemmit͡ɬ]||1/2 T||1.25 m|
|arm||cemacolli||[semaˈkolːi]||1/3 T||0.83 m|
|bone||cemomitl||[seˈmomit͡ɬ]||1/5 T||0.5 m|
|heart||cenyollotli||[senjoˈlːot͡ɬi]||2/5 T||1.0 m|
|hand||cemmatl||[ˈsemmat͡ɬ]||3/5 T||1.5 m|
Using their knowledge of tlalcuahuitl, Barbara J. Williams of the Department of Geology at the University of Wisconsin and María del Carmen Jorge y Jorge of the Research Institute for Applied Mathematics and FENOMEC Systems at the National Autonomous University of Mexico believe the Aztecs used a special type of arithmetic. This arithmetic (tlapōhuallōtl [t͡ɬapoːˈwalːoːt͡ɬ] ) the researchers called Acolhua [aˈkolwa] Congruence Arithmetic and it was used to calculate the area of Aztec people's land as demonstrated below:
|Field Id.||Side lengths a, b, c, d in (T)||Recorded Area (T²)||Calculated Area (T²)|
|Multiplication of two adjacent sides|
|1-207-31||20 + ht||19 + hd||20 + ht||19 + a||380||20 x 19 = 380|
|3-50-7||17||23||16||24||391||17 x 23 = 391|
|Average length of one pair of opposite sides times an adjacent side|
|4-27-16||42||12||40||11||451||11 x (42 +40)/2 = 11 x 41 = 451|
|5-12-2||52||21||56||13||884||52 x (21 + 13)/2 = 52 x 17 = 884|
|5-145-31||40||8||27||24||432||27 x (8 + 24)/2 = 27 x 16 = 432|
|Surveyors' Rule, A = (a + c)/2 x (b + d)/2|
|5-111-21||26||32||30||10||588||(26 + 30)/2 x (32 + 10)/2 = 28 x 21 = 588|
|5-46-4||23||15 + hd||25 + hd||11||312||(23 + 25)/2 + (15 + 11)/2 = 24 x 13 = 312|
|1-2-1||16||10||11||9||126||(16 + 11)/2 = 13.5ru = 14, (10 + 9)/2 = 9.5rd = 9,|
14 x 9 = 126
|Triangle Rule, A = (a x b)/2 + (c x d)/2, or (a x d)/2 + (b x c)/2|
|2-2-1||41||11||35||8 + a||366||(41 + 11)/2 = 225.5ru = 226, (35 x 8)/2 = 140, |
226 + 140 = 366
|2-30-6||24||16||25||24||492||(24 x 16)/2 + (24 x 25)/2 = 192 + 300 = 492|
|5-34-3||49||14||47||12 + a||623||(49 x 12)/2 + (14 x 47)/2 = 294 + 329 = 623|
|Plus-Minus Rule, one sidelength +1 or +2 times another sidelength -1 or -2|
|1-106-25||16||8||16||7||126||(16 - 2) x (7 + 2) = 14 x 9 = 126|
|5-139-30||18||19||13||13 + a||252||(19 - 1) x (13 + 1) = 18 x 14 = 252|
|1-189-27||14||6||13||6||75||(14 + 1) x (6 - 1) = 15 x 5 = 75|
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