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Translating abacus procedure to wikitables

awk code

BEGIN {
    FS="|";
    print "<div style=\"font-family:Courier; line-height: 1.10em;\">";
    print "{| class=\"wikitable\"";
    print "|+ Caption text";
    print "|-";
    print "! Abacus !! Comment";
}
{
    sub(/\ *$/,"",$1)
    gsub(/\ /,"\&nbsp;",$1);
    print "|-";
    print "| " $1;
    print "| " $2;
}
END {
    print "|}</div>";
}

Data used

 ABCDEFGHIJKLM|
    4567890123|Entering radicand starting in CD (first group)
  2           |First root digit in B
   -4         |Subtract square of B from first group
  2  567890123|Null remainder
  4  567890123|Doubling B. Appending next group to remainder
  41 567890123|5/4≈1, try 1 as next root digit
    -4        |Continue division by 41, subtract 1✕41 from EF
     -1|
  41 157890123|15 as remainder
  42 157890123|Double second root digit
  42 157890123|Append next group
  423157890123|157/42≈3, try 3 as next root digit
    -12       |Continue division by 423, subtract 3✕423 from E-H
     -06|
      -09|
  423 30990123|309 as remainder
  426 30990123|Double third root digit
  426 30990123|Append next group
     etc.|

Generated code

<div style="font-family:Courier; line-height: 1.10em;">
{| class="wikitable"
|+ Caption text
|-
! Abacus !! Comment
|-
| ABCDEFGHIJKLM
| 
|-
|    4567890123
| Entering radicand starting in CD (first group)
|-
|  2
| First root digit in B
|-
|   -4
| Subtract square of B from first group
|-
|  2  567890123
| Null remainder
|-
|  4  567890123
| Doubling B. Appending next group to remainder
|-
|  41 567890123
| 5/4≈1, try 1 as next root digit
|-
|    -4
| Continue division by 41, subtract 1✕41 from EF
|-
|     -1
| 
|-
|  41 157890123
| 15 as remainder
|-
|  42 157890123
| Double second root digit
|-
|  42 157890123
| Append next group
|-
|  423157890123
| 157/42≈3, try 3 as next root digit
|-
|    -12
| Continue division by 423, subtract 3✕423 from E-H
|-
|     -06
| 
|-
|      -09
| 
|-
|  423 30990123
| 309 as remainder
|-
|  426 30990123
| Double third root digit
|-
|  426 30990123
| Append next group
|-
|     etc.
| 
|}</div>

Generated table

After changing caption:

Starting the square root of 4.567890123

Abacus
Comment

ABCDEFGHIJKLM

   4567890123

Entering radicand starting in CD (first group)

 2

First root digit in B

  -4

Subtract square of B from first group

 2  567890123

Null remainder

 4  567890123

Doubling B. Appending next group to remainder

Note

 41 567890123

5/4≈1, try 1 as next root digit

   -4

Continue division by 41, subtract 1✕41 from EF

    -1

 41 157890123

15 as remainder

 42 157890123

Double second root digit

 42 157890123

Append next group

 423157890123

157/42≈3, try 3 as next root digit

   -12

Continue division by 423, subtract 3✕423 from E-H

    -06

     -09

 423 30990123

309 as remainder

 426 30990123

Double third root digit

 426 30990123

Append next group

    etc.

Abacus diagram

   9 18  8  0  0  1              9  9  9

╔═════════════════════════════════════════╗

║  │  │  │  ●  ●  ●  ●  ●  ●  ●  │  │  │  ║

║  │  │  │  │  │  │  │  │  │  │  │  │  │  ║

║  ●  ●  ●  │  │  │  │  │  │  │  ●  ●  ●  ║

╠═════════════════════════════════════════╣

║  ●  ●  ●  │  │  ●  │  │  │  │  ●  ●  ●  ║

║  ●  ●  ●  │  │  │  │  │  │  │  ●  ●  ●  ║

║  ●  ●  ●  ●  ●  │  ●  ●  ●  ●  ●  ●  ●  ║

║  ●  │  │  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ║

║  │  │  │  ●  ●  ●  ●  ●  ●  ●  │  │  │  ║

║  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  │  │  │  ║

║  │  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ║

╚═════════════════════════════════════════╝

   A  B  C  D  E  F  G  H  I  J  K  L  M

Caption text
Header text	Header text
9 18 8 0 0 1 9 9 9 ╔═════════════════════════════════════════╗ ║ │ │ │ ● ● ● ● ● ● ● │ │ │ ║ ║ │ │ │ │ │ │ │ │ │ │ │ │ │ ║ ║ ● ● ● │ │ │ │ │ │ │ ● ● ● ║ ╠═════════════════════════════════════════╣ ║ ● ● ● │ │ ● │ │ │ │ ● ● ● ║ ║ ● ● ● │ │ │ │ │ │ │ ● ● ● ║ ║ ● ● ● ● ● │ ● ● ● ● ● ● ● ║ ║ ● │ │ ● ● ● ● ● ● ● ● ● ● ║ ║ │ │ │ ● ● ● ● ● ● ● │ │ │ ║ ║ ● ● ● ● ● ● ● ● ● ● │ │ │ ║ ║ │ ● ● ● ● ● ● ● ● ● ● ● ● ║ ╚═════════════════════════════════════════╝ A B C D E F G H I J K L M	Example

Math

$x_{i}-(y_{i}+1)^{2}=x_{i}-y_{i}^{2}-2y_{i}-1<0$

Traditional Abacus Techniques

Table of content

Foreword
Traditional versus modern methods
The principle of least effort
Addition and subtraction
- Learning addition and subtraction
- Use of the 5th lower bead
Division
- Modern and traditional division; close relatives
- Guide to traditional division (帰除法)
- How to learn the division table
- Dealing with overflow
- Specialized division tables
- Division by powers of two
- Traditional division examples
Multiplication
Roots
- Square root
- Cube root
- A non-traditional method
Practicing without exercise sheets
- The 123456789 exercise
Abbreviated operations

Suanpan article (contrib)

The most mysterious and seemingly superfluous fifth lower bead, likely inherited from counting rods as suggested by the image above, was used to simplify and speed up addition and subtraction somewhat, as well as to decrease the chances of error^[1]. Its use was demonstrated, for example, in the first book devoted entirely to suanpan: Computational Methods with the Beads in a Tray (Pánzhū Suànfǎ 盤珠算法) by Xú Xīnlǔ 徐心魯 (1573, Late Ming Dynasty)^[2]. The following two animations show the details of this particular usage:^[3]

Use of the 5^th lower bead in addition according to the Panzhu Suanfa
Use of the 5^th lower bead in subtraction according to the Panzhu Suanfa

^ Chen, Yifu (2018). "The Education of Abacus Addition in China and Japan Prior to the Early 20th Century". Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Springer. pp. 243-. ISBN 978-3-319-73396-8.
^ Suzuki, Hisao (1982). "Zhusuan addition and subtraction methods in China". Kokushikan University School of Political Science and Economics (in Japanese). 57 – via Kokushikan.
^ "A short guide to the 5th lower bead" (PDF). 算盤 Abacus: Mystery of the bead. 2020. Archived (PDF) from the original on 2021-02-01. Retrieved 2021-07-07. {{cite web}}: |archive-date= / |archive-url= timestamp mismatch; 2021-01-26 suggested (help)

Subpages

Testing a reference to a subpage.

[1] Chen, Yifu (2018). "The Education of Abacus Addition in China and Japan Prior to the Early 20th Century". Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Springer. pp. 243-. ISBN 978-3-319-73396-8.

[2] Suzuki, Hisao (1982). "Zhusuan addition and subtraction methods in China". Kokushikan University School of Political Science and Economics (in Japanese). 57 – via Kokushikan.

[3] "A short guide to the 5th lower bead" (PDF). 算盤 Abacus: Mystery of the bead. 2020. Archived (PDF) from the original on 2021-02-01. Retrieved 2021-07-07. {{cite web}}: |archive-date= / |archive-url= timestamp mismatch; 2021-01-26 suggested (help)

[1]

[2]

[3]

Abacus	Comment
ABCDEFGHIJKLM
4567890123	Entering radicand starting in CD (first group)
2	First root digit in B
-4	Subtract square of B from first group
2 567890123	Null remainder
4 567890123	Doubling B. Appending next group to remainder	Note
41 567890123	5/4≈1, try 1 as next root digit
-4	Continue division by 41, subtract 1✕41 from EF
-1
41 157890123	15 as remainder
42 157890123	Double second root digit
42 157890123	Append next group
423157890123	157/42≈3, try 3 as next root digit
-12	Continue division by 423, subtract 3✕423 from E-H
-06
-09
423 30990123	309 as remainder
426 30990123	Double third root digit
426 30990123	Append next group
etc.