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xabacus

NAME

xabacus - Abacus X widget

SYNOPSIS

/usr/games/xabacus [-geometry [{width}][x{height}][{+-}{xoff}[{+-}{yoff}]]] [-display [{host}]:[{vs}]] [-[no]mono] [-[no]{reverse|rv}] [-{foreground|fg} {color}] [-{background|bg} {color}] [-bead {color}] [-frame {color}] [-rail {color}] [-{border|bd} {color}] [-delay msecs] [-[no]sound] [-bumpSound {filename}] [-moveSound {filename}] [-[no]demo] [-[no]script] [-demopath {path}] [-{demofont|demofn} {fontname}] [-{demoforeground|demofg} {color}] [-[no]vertical] [-colorScheme {int}] [-[no]slot] [-[no]diamond] [-railIndex {int}] [-[no]torient] [-[no]borient] [-tnumber {int}] [-bnumber {int}] [-tfactor {int}] [-bfactor {int}] [-tspaces {int}] [-bspaces {int}] [-tpiece {int}] [-bpiece {int}] [-tpiecePercent {int}] [-bpiecePercent {int}] [-shiftPercent {int}] [-subdeck {int}] [-subbead {int}] [-[no]sign] [-decimalPosition {int}] [-groupSize {int}] [-rails {int}] [-base {int}] [-anomaly {int}] [-shiftAnomaly] [-anomalySq {int}] [-shiftAnomalySq] [-displayBase {int}] [-[no]romanNumerals] [-[no]group] [-{chinese|japanese|korean|roman|russian|danish|other}] [-{it|uk|fr}] [-version]

DESCRIPTION

This is an implementation of the classic Chinese abacus (Saun-pan) which has its origins in the 12th century.

The device has two decks. Each deck, separated by a partition, normally has 13 rails on which are mounted beads. Each rail on the top deck contains 1 or 2 beads, and each rod on the bottom deck contains 4 or 5 beads. Each bead on the upper deck has a value of five, while each bead on the lower deck has value of one. Beads are considered counted, when moved towards the partition separating the decks, i.e. to add a value of one, a bead in the bottom deck is moved up, and to add a value of 5, a bead in the top deck is moved down.

The basic operations of the abacus are addition and subtraction. Multiplication can be done by mentally multiplying the digits and adding up the intermediate results on the abacus. Division would be similar where the intermediate results are subtracted. There are techniques like using your thumb and forefinger which does not apply with mouse entry. Also with multiplication, one can carry out calculations on different parts of the abacus for scratch work, here it is nice to have a long abacus.

The pre-WWII Japanese abacus (Soroban) (or Korean Supan) is similar to the Chinese abacus but has only one bead per rail on the top deck. The later Japanese abacus was further simplified to have only 4 beads per rail on the bottom deck.

The Roman hand-abacus predates the Chinese abacus and is very similar to the later Japanese abacus, but seems to have fallen out of use with the Fall of the Roman Empire (at least 3 are in existence). The Roman abaci are brass plates where the beads move in slots. In addition to the normal 7 columns of beads, they generally have 2 special columns on the right side. In two examples: the first special column was for 12ths (12 uncia (ounces) = 1 as), and had one extra bead in the bottom deck. Also the last column was a combination of halves, quarters, and twelfths of an ounce and had no slot in the top deck and 4 beads at the bottom (beads did not have to come to the top to be counted but at one of 3 marked points where the top bead was for halves, the next bead for quarters, and the last two beads for twelfths). In another surviving example: the 2 special columns were switched and the combination column was broken into 3 separate slots. If available, decimal input is ignored.

The Russian abacus was invented in the 17th century, here the beads are moved from right to left. It has colored beads in the middle for ease of use. Quarters represent 1/4 Rubles and are only present historically on the Russian abacus (Schoty). Some of the older Schoty have a extra place for the 1/4 Kopek (quarter percent) as well as the 1/4 Ruble (quarter).

The Danish abacus was used in the early 20th century in elementary schools as a teaching aid.

The Mesoamerican Nepohualtzintzin is a Japanese abacus base 20. The Mesoamericans had base 20 with the exception of the 3rd decimal place where instead of 20*20=400 the third place marked 360 and the 4th place was 20*360, etc.. They independently created their own zero (only Babylon (base 60) and India (base 10) have done this) but the anomaly took away its true power.

An easy way of figuring out time in seconds given hours, minutes, and seconds, can be done on the abacus with special anomaly "watch" settings.

The Chinese Solid-and-Broken-Bar System is a base 12 numbering system and not really an abacus. When the abacus is setup in this way though (topFactor 3, bottomNumber 2, base 12, displayBase 12), it is easy to relate the two.

The signed bead is an invention of the author, and is not present on any historical abacus (to his knowledge) and is used to represent negatives. "New & Improved" abacus models have two auxiliary decks stacked above the principal deck that enable multiplication, division, square-root, and cube-root computations to be performed with equal ease as addition and subtraction.

FEATURES

Click "mouse-left" button on a bead you want to move. The beads will shift themselves to vacate the area of the column that was clicked.

Click "mouse-right" button, or press "C" or "c" keys, to clear the abacus.

Press "O" or "o" keys to toggle the demo mode.

Press "I" or "i" keys to increment the number of rails.

Press "D" or "d" keys to decrement the number of rails.

Press "F" or "f" keys to switch between Chinese, Japanese, Korean, Roman, and Russian formats.

Press "E" or "e" keys to switch between it, uk, and fr museum formats.

Press "M" or "m" keys to toggle Roman Numerals.

Press "S" or "s" keys to toggle the availability of a sign bead.

Press "U" or "u" keys to toggle the availability of quarter beads. (Mutually exclusive to twelfth beads). Intended for the Russian Abacus.

Press "P" or "p" keys to toggle the availability of quarter percent beads. (Dependent on quarter beads (or twelfth beads). Intended for the older Russian Abacus.

Press "T" or "t" keys to toggle the availability of twelfth beads. (Mutually exclusive to quarter beads). Intended for the Roman Abacus.

Press "B" or "b" keys to toggle the availability of subdecks. (Dependent on twelfth beads (or quarter beads) and Roman format). Intended for the Roman Abacus.

Press "L" or "l" keys to toggle the availability of anomaly bars. Intended to be used with Japanese Abacus and base 20 for the Mesoamerican Abacus. (Mutually exclusive to watch bars).

Press "W" or "w" keys to toggle the availability of watch bars. Intended to represent seconds where hours and minutes can be set. (Mutually exclusive to anomaly bars).

Press ">" or "." keys to speed up the movement of beads.

Press "<" or "," keys to slow down the movement of beads.

Press "@" key to toggle the sound.

Press "Esc" key to hide program.

Press "Q", "q", or "CTRL-C" keys to kill program.

The abacus may be resized. Beads will reshape depending on the room they have. Demo Mode: In this mode, the abacus is controlled by the program. When started with the demo option, a second window is presented that should be placed directly below the abacus-window. Descriptive text, and user prompts are displayed in this window. Pressing 'q' during the demo will quit it. Clicking the left mouse-button with the pointer in the window will restart the demo (beginning of current lesson).

OPTIONS

-geometry {+|-}X{+|-}Y

This option sets the initial position of the abacus window (resource name "geometry").

-display host:dpy

This option specifies the X server to contact.

-[no]mono

This option allows you to display the abacus window on a color screen as if it were monochrome (resource name "mono").

-[no]{reverse|rv}

This option allows you to see the abacus window in reverse video (resource name "reverseVideo").

-{foreground|fg} color

This option specifies the foreground of the abacus window (resource name "foreground").

-{background|bg} color

This option specifies the background of the abacus window (resource name "background").

-frame color

This option specifies the foreground of the frame (resource name "frameColor").

-rail color

This option specifies the foreground of the rails (resource name "railColor").

-bead color

This option specifies the foreground of the beads (resource name "beadColor").

-{border|bd} color

This option specifies the foreground of the bead border (resource name "borderColor").

-delay msecs

This option specifies the number of milliseconds it takes to move a bead or a group of beads one space (resource name "delay").

-[no]sound

This option specifies if a sliding bead should make a sound or not (resource name "sound").

-bumpSound filename

This option specifies the file for the bump sound (resource name "bumpSound").

-moveSound filename

This option specifies the file for the move sound (resource name "moveSound").

-[no]demo

This option specifies to run in demo mode. In this mode, the abacus is controlled by the current lesson (resource name "demo"). When started with the demo option, a window contains descriptive text, and user prompts are displayed in this window. Pressing 'q' during the demo will quit it. Clicking the left mouse-button with the pointer in the window will restart the demo (beginning of current lesson). The demo uses Abacus1.les for the first Chinese Abacus lesson, Abacusjp1.les for the first Japanese (and Roman) Abacus lesson, Abacusko1.les for the Korean Abacus, and Abacusru1.les for the Russian Abacus.

-[no]script

This option specifies to log application to stdout, every time the user clicks to move the beads (resource name "script"). The output is a set of deck, rail, beads added or subtracted, and the number of text lines (4). This can be edited to add text to the lesson and used as a new demo keeping the generated numbers and the number of lines constant. If you want to add a "do nothing", the first line generated is an example of that. For example: "xabacus -script > Abacus5.les"

-demopath path

This option specifies the path for the demo, possibly something like /usr/local/share/games/xabacus (resource name "demoPath"). It initially looks for Abacus1.les. If it finds that, it will later look for Abacus2.les, etc.

-demofont fontstring

This option specifies the font for the explanatory text that appears in the secondary window, during the demo. The default font is 18 point Times-Roman (-*-times-*-r-*-*-*-180-*). The alternate font is 8x13.

-demofg color

This option specifies the foreground of the abacus demo window (resource name "demoForeground").

-demobg color

This option specifies the background of the abacus demo window (resource name "demoBackground").

-[no]vertical

This option allows you to set the abacus to allow a Russian orientation (resource name "vertical").

-colorScheme int

This option specifies the color scheme for the abacus (resource name "colorScheme") where 0-> none, 1-> color middle (2 beads beads but if odd color 1 bead), 2-> color first of group, 3-> both 1 and 2, 4-> color first half (but if odd color middle bead).

-[no]slot

This option allows you to have either slots or rails (resource name "slot").

-[no]diamond

This option allows you to have either diamond or round beads (resource name "diamond").

-railIndex int

This option specifies the index of color for the rails of the abacus (resource name "railIndex") where a value is 0 or 1.

-[no]torient

This option specifies the orientation of the beads on top (resource name "topOrient").

-[no]borient

This option specifies the orientation of the beads on bottom (resource name "bottomOrient").

-tnumber int

This option specifies the number of beads on top (resource name "topNumber").

-bnumber int

This option specifies the number of beads on bottom (resource name "bottomNumber").

-tfactor int

This option specifies the multiply factor for the beads on top (resource name "topFactor").

-bfactor int

This option specifies the multiply factor for the beads on bottom (resource name "bottomFactor").

-tspaces int

This option specifies the number of spaces on top (resource name "topSpaces").

-bspaces int

This option specifies the number of spaces on bottom (resource name "bottomSpaces").

-tpiece int

This option specifies the number of pieces on top (resource name "topPiece").

-bpiece int

This option specifies the number of pieces on bottom (resource name "bottomPiece").

-tpiecePercent int

This option specifies the number of piece percents on top (resource name "topPiecePercent").

-bpiecePercent int

This option specifies the number of piece percents on bottom (resource name "bottomPiecePercent").

-shiftPercent int

This option specifies the shift of rails for piece percents and also may influence the precision of the calculation (resource name "shiftPercent").

-subdeck int

This option specifies the special subdecks column (resource name "subdeck").

-subbead int

This option specifies the special subbeads (resource name "subbead").

-[no]sign

This option allows you to set the abacus to allow negatives (resource name "sign").

-decimalPosition int

This option specifies the number of rails to the right of the decimal point (normally 2) (resource name "decimalPosition").

-groupSize int

This option specifies the group size to the left of the decimal point (normally 3) (resource name "groupSize").

-rails int

This option specifies the number of rails (resource name "rails").

-base int

This option specifies the base used on abacus (default is base 10) (resource name "base"). By default, one has to set the format mode to not be Other for this to work (unless you know what you are

-anomaly int

This option specifies the offset from the base for a multiplicative factor of the rail with the anomaly (if none, this is set to 0) (resource name "anomaly").

-anomalyShift int

This option specifies the offset from decimal point for the anomaly (usually 2) (resource name "anomalyShift").

-anomalySq int

This option specifies the offset from base for the second anomaly (if none, this is set to 0) (resource name "anomalySq").

-anomalySqShift int

This option specifies the offset in rails from the first anomaly (usually 2) (resource name "anomalySqShift"). doing).

-displayBase int

This option specifies the base displayed (default is base 10) (resource name "displayBase"). If this is different then "base" then it is implemented using "long long" and the calculation is limited by its bounds. Also the fractional part does not scale with the "displayBase" so if the "displayBase" is greater than the "base" it looses some precision. Also no rounding is done.

-[no]romanNumerals

This option allows you to set the abacus to allow Roman Numerals (resource name "romanNumerals"). Roman Numerals above 3999 are normally represented with bars on top, due to ASCII constraints this is represented instead in lower case (historically case was ignored). Roman Numerals above 3,999,999 were not represented historically. Roman numerals change with displayBase in an "experimental" way. When used with twelfths and subdecks, named fraction symbols are used. Due to ASCII constraints the sigma is represented as E, the backwards C is represented as a Q, the mu as a u, and the Z with a - through the center as a z. If available, decimal input is ignored.

-[no]group

This option allows you to group the displayed digits for readability (resource name "group").

-chinese

This option specifies the format on the abacus (resource name "format") to "Chinese" for the Chinese Saun-pan.

-japanese

This option specifies the format on the abacus (resource name "format") to "Japanese" for the Japanese post-WWII Soroban. This is also similar to the Roman Hand Abacus.

-korean

This option specifies the format on the abacus (resource name "format") to "Korean" for the Korean Supan or Japanese pre-WWII Soroban.

-roman

This option specifies the format on the abacus (resource name "format") to "Roman" for the Roman Hand Abacus, note beads move in slots. To complete, specify romanNumerals".

-russian

This option specifies the format on the abacus (resource name "format") to "Russian" for the Russian Schoty. To complete, specify piece" to be 4, for the older Schoty also specify piecePercent" to be 4.

-danish

This option specifies the format of the abacus (resource name "format") to "Danish" for the Danish Elementary School Abacus teaching aid.

-other

This option specifies the format on the abacus (resource name "format") to "Other". This option specifies a format that is more configurable by using resources, since there are few rules to govern its behavior.

-it

This option specifies the subformat of the abacus in Museum of the Thermae, Rome.

-uk

This option specifies the subformat of the abacus in British Museum in London.

-fr

This option specifies the subformat of the abacus in Cabinet de medailles, Bibliotheque nationale, Paris.

-version

This option tells you what version of xabacus you have.

REFERENCES

Luis Fernandes http://www.ee.ryerson.ca/~elf/abacus/

Lee Kai-chen, How to Learn Lee's Abacus, 1958, 58 pages.

Abacus Guide Book, 57 pages.

Georges Ifrah, The Universal History of Numbers, Wiley Press 2000, pp 209-211, 288-294.

Review of the above: http://www.ams.org/notices/200201/rev-dauben.pdf

David Eugene Smith, History of Mathematics Volume II, Dover Publications, Inc 1958, pp 156-195.

SEE ALSO

X(1), xcubes(6), xtriangles(6), xhexagons(6), xmlink(6), xbarrel(6), xpanex(6), xmball(6), xpyraminx(6), xoct(6), xrubik(6), xskewb(6), xdino(6)

COPYRIGHTS

® Copyright 1994-2007, David Albert Bagley

Luis Fernandes, <elf@ee.ryerson.ca> wrote an independent program (xabacus 1.00) with a demo mode and postscript file. I tried, with his permission, to take the best features of both into one program. Also, I had help with some of the abacus in the Java version by Sarat Chandran, <aratcmahadevan@yahoo.com> and some of these ideas were ported back into this X version.

BUG REPORTS AND PROGRAM UPDATES

Send bugs (or their reports, or fixes) to the author:

David Albert Bagley, <bagleyd@tux.org>

The latest version is currently at:

http://www.tux.org/~bagleyd/abacus.html
ftp://ibiblio.org/pub/Linux/apps/math