User:Jccsvq/sandbox
Translating abacus procedure to wikitables[edit]
awk code[edit]
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(/\ /,"\ ",$1);
print "|-";
print "| " $1;
print "| " $2;
}
END {
print "|}</div>";
}
Data used[edit]
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[edit]
<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[edit]
After changing caption:
| 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[edit]
9 18 8 0 0 1 9 9 9
╔═════════════════════════════════════════╗
║ │ │ │ ● ● ● ● ● ● ● │ │ │ ║
║ │ │ │ │ │ │ │ │ │ │ │ │ │ ║
║ ● ● ● │ │ │ │ │ │ │ ● ● ● ║
╠═════════════════════════════════════════╣
║ ● ● ● │ │ ● │ │ │ │ ● ● ● ║
║ ● ● ● │ │ │ │ │ │ │ ● ● ● ║
║ ● ● ● ● ● │ ● ● ● ● ● ● ● ║
║ ● │ │ ● ● ● ● ● ● ● ● ● ● ║
║ │ │ │ ● ● ● ● ● ● ● │ │ │ ║
║ ● ● ● ● ● ● ● ● ● ● │ │ │ ║
║ │ ● ● ● ● ● ● ● ● ● ● ● ● ║
╚═════════════════════════════════════════╝
A B C D E F G H I J K L M
| Header text | Header text |
|---|---|
9 18 8 0 0 1 9 9 9 |
Example |
Math[edit]
Traditional Abacus Techniques[edit]
Table of content[edit]
- 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)[edit]
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 5th lower bead in addition according to the Panzhu Suanfa -
Use of the 5th 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[edit]
Testing a reference to a subpage.