About Abacus

The Abacus Genius students initially use an a abacus which is very similar to the soroban(Japanese Abacus) but it has 17 rods.  The abacus is used while lying flat on the table. After 24 hours of classroom training and subsequent home training the children can develop the image of the abacus (soroban) in the right brain and move the beads by using corresponding manipulations for addition. And over a period of 2 years…

A brief view on development of Numbers(Numeric Systems)

Men of ancient times used sign language or sounds to communicate with each other. These sounds were only oral and did not have any corresponding signs or signage(alphabets). It was later that each sound was given a shape in the form of alphabets.
Similarly when men counted they used sounds and their finger for signs. The roman numbers are a classic example of these if we analyse them closely.

Arabic Number

Roman Number

Explanation of the signage

1

I

One finger

2

II

Two fingers

4

IV

Five but one finger taken to left hand

5

V

Thumb and index finger

6

VI

Five and additional finger

8

VIII

Five and the remaining fingers on the hand

10

X

Both hands full so 2 fingers crossed or 2fives while one is inverted

But again they ran to a road block as they could not  calculate any numbers larger than 10.

The Arabic number also did not have the zero and could not proceed any further. This being the case when the tenth came along the ancient man would make a mark of the floor, or use a stone to indicate each ten.

ABACUS

The word ‘abacus’ derives from the Greek word ‘abax’ or ‘abakon’ meaning table or tablet, which originated from the Semitic word ‘abaq’ meaning sand. The plural of ‘abacus’ is ‘abacuses’ or ‘abaci’. And a user is called abacist.
The first abacus was almost certainly based on a flat stone covered with sand or dust. Words and letters were drawn in the sand; eventually numbers were added and pebbles used to aid calculations. In outdoor markets of those times, the simplest counting board involved drawing lines in the sand with ones fingers or with a stylus, and placing pebbles between those lines as place-holders representing numbers (the spaces between 2 lines would represent the units 10s, 100s, etc.). The more affluent people, could afford small wooden tables having raised borders that were filled with sand (usually coloured blue or green). A benefit of these counting boards on tables, was that they could be moved without disturbing the calculation— the table could be picked up and carried indoors.
As each civilizations grew they were able to develop an abacus that met their needs the best. The Babylonians used this dust abacus as early as 2400 BC. The origin of the counter abacus with strings is obscure, but IndiaMesopotamia or Egypt are seen as probable points of origin. China played an essential part in the development and evolution of the abacus.

The evolution of the abacus can be divided into three ages: Ancient Times, Middle Ages, and Modern Times. The time-line below traces the developing abacus from its beginnings from 500 B.C., to the present. It can be noted like every other development the growth of the abacus was slow during the first part of its life but the last millennium it grew at changed at a rapid pace.

Babylonian abacus
Babylonians may have used the abacus for the operations of addition and subtraction. However, this primitive device proved difficult to use for more complex calculations. Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.

Egyptian abacu
The use of the abacus in ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the manner of this disk’s usage by the Egyptians was opposite in direction when compared with the Greek method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered, casting some doubt over the extent to which this instrument was used.

Grecian  abacus
A tablet found on the Greek island Salamis in 1846 dates back to 300 BC, making it the oldest counting board discovered so far. This is known as the Salamis TabletIt is a slab of white marble 149 cm long, 75 cm wide, and 4.5 cm thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semi-circle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semi-circle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

Roman  abacus
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles, calculi, were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens, hundreds etc. as in the Roman numeral system. This system of ‘counter casting’ continued into the late Roman empire and in medieval Europe, and persisted even into the nineteenth century.
In addition to the more common method using loose counters, several specimens have been found of a Roman abacus, shown here in reconstruction. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. (Please find the picture)
The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives—five units, five tens etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman ounces.
For more details and greater understanding of usage and workings click here – Roman Abacus.

Chinese  abacus
The Chinese abacus was called a Suanpan. It is about 20 cm tall and it comes in various widths depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal and hexadecimal computation. Modern abacuses have one bead on the top deck and four beads on the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. If you move them high, you count their value. If you move them down, you don’t count their value. The suanpan can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center.
Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. For more details and greater understanding of usage and workings click here – Suanpan.

Japanese  abacus (Soroban)
soroban (meaning “Counting tray”) is a Japanese-modified version of the Chinese abacus. It is devised from the suanpan, imported from China to Japan through the Korean peninsula in the 15th century. The modification was that the Japanese took 2 beads from each rod, i.e. one from the upper deck and another from the lower deck. Like the suanpan, the soroban is still used in Japan today, even with the proliferation, practicality, and affordability of pocket electronic calculators.

Russian  abacus (Schoty)
The Russian abacus, the schoty usually has a single slanted deck, with ten beads on each wire (except one wire which has four beads). This wire is usually near the user. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, in order to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually have a colour different from the other 8 beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.
The Russian abacus is still in use today in shops and markets throughout the former Soviet Union, although it is no longer taught in most schools.

School abacus
Around the world, abaci have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic. In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.
The type of abacus shown here is often used to represent numbers without the use of place value. Each bead and each wire has the same value and used in this way it can represent numbers up to 100.

The most significant educational advantage of using an abacus, rather than loose beads or counters, when practicing counting and simple addition is that it gives the student an awareness of the groupings of 10 which are the foundation of our number system. Although adults take this base 10 structure for granted, it is actually difficult to learn. Many 6-year-olds can count to 100 by rote with only a slight

Abacus Genius
The Abacus Genius students initially use an abacus which is very similar to the soroban(Japanese Abacus) but it has 17 rods.  The abacus is used while lying flat on the table. After 24 hours of classroom training and subsequent home training the children can develop the image of the abacus (soroban) in the right brain and move the beads by using corresponding manipulations for addition. And over a period of 2 years students  will be skilled to do all operations like addition, subtraction, multiplication & division. So in reality unlike all the types of abacuses (abaci) discussed above this is unique as this involves real children who can perform the work of the abacus using their well trained brain. For more details of the program click on course