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User:Jccsvq/sandbox

< User:Jccsvq

Tempo edit

137/2
 ABCD
 --+-
 137
   7
  +35
  3
 +15
 1
+05
 --+-
 0685
68.5
137/4
 ABCDE
 --+--
 137
   7
  +175
  3
 +075
 1
+025
 --+--
 03425
34.25
137/8
 ABCDEF
 --+---
 137
   7
  +0875
  3
 +0375
 1
+0125
 --+---
 017125
17.125
137/16
 ABCDEF
 --+---
 137
   7
  +4375
  3
 +1875
 1
+0625
 -+----
 085625
8.5625
137/32
 ABCDEFG
 --+----
 137
   7
  +21875
  3
 +09375
 1
+03125
 -+-----
 0428125
4.28125
137/64
 ABCDEFGH
 --+-----
 137
   7 Borrar 7 en C
  +109375
  3 Borrar 3 en B
 +046875
 1 Borrar 1 en A
+015625
 -+------
 02140625
2.140625
"+" indica la posición de la columna unidad antes y después de la operación.

1-digit Addition/Subtraction types edit

1-digit addition: type 1-digit subtraction: type
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
+1 1 1 1 1 2 1 1 1 1 3 -1 3 1 1 1 1 2 1 1 1 1
+2 1 1 1 2 2 1 1 1 3 3 -2 3 3 1 1 1 2 2 1 1 1
+3 1 1 2 2 2 1 1 3 3 3 -3 3 3 3 1 1 2 2 2 1 1
+4 1 2 2 2 2 1 3 3 3 3 -4 3 3 3 3 1 2 2 2 2 1
+5 1 1 1 1 1 3 3 3 3 3 -5 3 3 3 3 3 1 1 1 1 1
+6 1 1 1 1 3 3 3 3 3 3 -6 3 3 3 3 3 3 1 1 1 1
+7 1 1 1 3 3 3 3 3 3 3 -7 3 3 3 3 3 3 3 1 1 1
+8 1 1 3 3 3 3 3 3 3 3 -8 3 3 3 3 3 3 3 3 1 1
+9 1 3 3 3 3 3 3 3 3 3 -9 3 3 3 3 3 3 3 3 3 1
0 1 2 3 4 5 6 7 8 9
+1 1 1 1 1 2 1 1 1 1 3
+2 1 1 1 2 2 1 1 1 3 3
+3 1 1 2 2 2 1 1 3 3 3
+4 1 2 2 2 2 1 3 3 3 3
+5 1 1 1 1 1 3 3 3 3 3
+6 1 1 1 1 3 3 3 3 3 3
+7 1 1 1 3 3 3 3 3 3 3
+8 1 1 3 3 3 3 3 3 3 3
+9 1 3 3 3 3 3 3 3 3 3


0 1 2 3 4 5 6 7 8 9
-1 3 1 1 1 1 2 1 1 1 1
-2 3 3 1 1 1 2 2 1 1 1
-3 3 3 3 1 1 2 2 2 1 1
-4 3 3 3 3 1 2 2 2 2 1
-5 3 3 3 3 3 1 1 1 1 1
-6 3 3 3 3 3 3 1 1 1 1
-7 3 3 3 3 3 3 3 1 1 1
-8 3 3 3 3 3 3 3 3 1 1
-9 3 3 3 3 3 3 3 3 3 1
q1 d1
10000 1109889
20000 739889
30000 369889
40000 -111
50000 -370111
60000 -740111
70000 -1110111
80000 -1480111
90000 -1850111

SANGA edit

 
Proto-Cuneiform tablet: administrative account of barley distribution with cylinder seal impression of a male figure, hunting dogs, and boars. Probably from the city of Uruk. Jemdet-Nasr period circa 3100 –2900 BCE

 

 
"SANGA" character.

The "SANGA" character is believed to be a pictorial representation of a Sumerian abacus.


Woods, Christopher (2017), "The Abacus in Mesopotamia: Considerations from a Comparative Perspective", The First Ninety Years: A Sumerian Celebration in Honor of Miguel Civil, De Gruiter, ISBN 9781501511738 {{citation}}: Unknown parameter |editor1first= ignored (|editor-first1= suggested) (help); Unknown parameter |editor1last= ignored (|editor-last1= suggested) (help); Unknown parameter |editor2first= ignored (|editor-first2= suggested) (help); Unknown parameter |editor2last= ignored (|editor-last2= suggested) (help); Unknown parameter |editor3first= ignored (|editor-first3= suggested) (help); Unknown parameter |editor3last= ignored (|editor-last3= suggested) (help)

Diagrams edit

Write caption here!
A B C D E F G H I
                     
T T T T T T T T 1


Write caption here!
A B C D E F G H I K J L M
                             
9 18 9 0 0 1 0 0 0 0 9 9 9


5+2 abacus number representation
A B C D E F G H I J K L
                           
0 1 2 3 4 5 5 6 7 8 9 10
5+2 abacus number representation (cont.)
A B C D E F G H I J K L
                           
10 11 12 13 14 15 15 16 17 18 19 20
Starting division 998001÷999
A B C D E F G H I J K L M
                             
9 9 8 0 0 1 9 9 9
Just after applying division rule 9/9>9+9
A B C D E F G H I J K L M
                             
9 18b 8 0 0 1 9 9 9

Diagrams 2 edit

A A
   A + 1 =    
4 5


text

A B A B
     B + 1 =      
0 9 1 0
Write caption here!
A B A B
     B+5 =     
4 6 F 1

text

Write caption here!
A B A B
     B + 5 =     
9 6 T 1

text

Tables edit

First 3 digits of   preparing the dividend
Abacus Comment
ABCDEFGHIJKL
 4567890123 Enter x aligning digit pairs from AB, CD, etc.
-4 Subtracting 2^2 from first group
  567890123
  2839450615 Halving remainder and rest of digits pairsa
2 2839450615 Entering first root digit in A
21 Dividing BCD by A
 -2
  -05 Subtracting B^2/2=0.5 from CDE
21 789450615
213789450615 Dividing CDEF by AB
  -6
   -3
    -45 Subtracting C^2/2=4.5 from CEFG
213154950615
    etc.

^a as explained in Chapter: [[../../Division/Division by powers of two/|Division by powers of two]].


First 3 digits of   preparing the dividend
Abacus Comment
ABCDEFGHIJKL
 4567890123 Enter x aligning digit pairs from AB, CD, etc.
-4 Subtracting 2^2 from first group
  567890123
  2839450615 Halving remainder and rest of digits pairsa
2 2839450615 Entering first root digit in A
21 Dividing BCD by A
 -2
  -05 Subtracting B^2/2=0.5 from CDE
21 789450615
213789450615 Dividing CDEF by AB
  -6
   -3
    -45 Subtracting C^2/2=4.5 from CEFG
213154950615
    etc.

Contributors edit

User Jccsvq (discuss•contribs) has contributed the base or initial text of this book by adapting some of his writings from his personal website jccAbacus.

Testing notes... edit

Article texta more textb more text c.

  • Bulleted textb
  • Bulleted textc.

(intervening text...)

Notes edit

  • ^a Text for note a.
  • ^b Text for note b.
  • ^c Text for note c (with extended highlighting).
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