View source for Tlalcuahuitl

'''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|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 || [[Social:Nahuatl|Nahuatl]] || IPA || Fraction of ''Tlalcuahuitl'' || Metric Equivalent <br>where 1 T = 2.5 m
|-
|[[File:Cemmitl one half of tlalcuahuitl Aztec glyph.png|20px|arrow glyph]]||arrow||cemmitl||{{IPA-nah|ˈsemmit͡ɬ|}}||1/2 T||1.25 m
|-
|[[File:Cemacolli one third tlalcuahuitl Aztec glyph.png|17px|arm glyph]]||arm||cemacolli||{{IPA-nah|semaˈkolːi|}}||1/3 T||0.83 m
|-
|[[File:Cemomitl one fifth of tlalcuahutil Aztec glyph.png|20px|bone glyph]]||bone||cemomitl||{{IPA-nah|seˈmomit͡ɬ|}}||1/5 T||0.5 m
|-
|[[File:Cenyollotli two fifths of a tlalcuahuitl Aztec glyph.png|20px|heart glyph]]||heart||cenyollotli||{{IPA-nah|senjoˈlːot͡ɬi|}}||2/5 T||1.0 m
|-
| [[File:Cemmatl thee fifths of a tlalcuahuitl.png|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|arithmetic]]. This arithmetic (''tlapōhuallōtl'' {{IPA-nah|t͡ɬapoːˈwalːoːt͡ɬ|}}) the researchers called Acolhua {{IPA-nah|aˈkolwa|}} Congruence Arithmetic and it was used to calculate the [[Area|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 = 13.5[[Rounding|ru]] = 14, (10 + 9)/2 = 9.5[[Rounding|rd]] = 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 = 225.5[[Rounding|ru]] = 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
|-
|}

==See also==
* meter
* [[Foot (unit)|feet]]

==References==
<references />

[[Category:Units of length]]

{{Sourceattribution|Tlalcuahuitl}}