{{Short description|Aztec unit of measurement}} '''Tlalcuahuitl''' {{IPA|nah|t͡ɬaɬˈkʷawit͡ɬ|}} or '''land rod'''<ref name="Acolhua" /> also known as a '''cuahuitl''' {{IPA|nah|ˈkʷawit͡ɬ|}} was an Aztec unit of measuring distance that was approximately {{convert|2.5|m|ft|abbr=on}},<ref name="Jorge" >Jorge, M et al. (2011). ''Mathematical accuracy of Aztec land surveys assessed from records in the Codex Vergara. PNAS:'' University of Michigan.</ref> {{convert|6|ft|m|abbr=on}} to {{convert|8|ft|m|abbr=on}}<ref name="dic" /> or {{convert|7.5|ft|m|abbr=on}} long.<ref name="dic" >''Nahuatl Dictionary.'' (1997). Wired Humanities Project. Retrieved September 8, 2012, from [http://whp.uoregon.edu/dictionaries/nahuatl/index.lasso link].</ref>
The abbreviation used for ''tlalcuahuitl'' is (T) and the unit square of a ''tlalcuahuitl'' is (T²).<ref name="Acolhua"/>
==Subdivisions of tlalcuahuitl== {| class="wikitable" style="text-align: center; width: 500px; height: 25px;" |+ Subdivisions of ''Tlalcuahuitl''<ref name="Acolhua" /> |- !Glyph || English || Nahuatl || IPA || Fraction of ''Tlalcuahuitl'' || Metric Equivalent <br>where 1 T = 2.5 m |- |20px|arrow glyph||arrow||cemmitl||{{IPA|nah|ˈsemmit͡ɬ|}}||1/2 T||1.25 m |- |17px|arm glyph||arm||cemacolli||{{IPA|nah|semaˈkolːi|}}||1/3 T||0.83 m |- |20px|bone glyph||bone||cemomitl||{{IPA|nah|seˈmomit͡ɬ|}}||1/5 T||0.5 m |- |20px|heart glyph||heart||cenyollotli||{{IPA|nah|senjoˈlːot͡ɬi|}}||2/5 T||1.0 m |- | 20px|hand glyph||hand||cemmatl||{{IPA|nah|ˈsemmat͡ɬ|}}||3/5 T||1.5 m |- |}
==Acolhua Congruence Arithmetic== 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'' {{IPA|nah|t͡ɬapoːˈwalːoːt͡ɬ|}}) the researchers called Acolhua {{IPA|nah|aˈkolwa|}} Congruence Arithmetic and it was used to calculate the area of Aztec people's land as demonstrated below:<ref name="Acolhua" >Williams, B.J. & Jorge, M. (2008). Aztec Arithmetic Revisited: land-Area Algorithms and Acolhua Congruence Arithmetic. In ''Science (320)''.</ref>
{| class="wikitable" style="text-align: center; width: 700px; height: 25px;" |+ Calculation Examples Yielding Acolhua Recorded Area<ref name="Acolhua" /> |- !Field Id. !colspan="4"| Side lengths a, b, c, d in (T) ! Recorded Area (T²) ! Calculated Area (T²) |- |colspan="7"| 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 |- |colspan="7"| 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 |- |colspan="7"| 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,<br> 14 x 9 = 126 |- |colspan="7"| 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, <br>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 |- |colspan="7"| 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 |- |}
==References== <references />
Category:Units of length Category:Aztec mathematics