The frame of the abacus has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck. Beads are considered counted, when moved towards the Beam— the piece of the abacus frame that separates the two decks. After 5 beads are counted in the lower deck, the result is "carried" to the upper deck; after both beads in the upper deck are counted, the result 10 is then carried to the left-most adjacent column.
The right-most column is the ones column; the next adjacent to the left is the tens column; the next adjacent to the left is the hundreds column, and so on. Floating point calculations are performed by designating a space between 2 columns as the decimal-point and all the rows to the right of that space represent fractional portions while all the rows to the left represent whole number digits.
Your browser does not support Java. The Java version of the abacus is a limited simulation of the real device because the fingering technique is completely obfuscated by the mouse. Abacus Apps on touch-screen tablets are better simulations. It is difficult to imagine counting without numbers, but there was a time when written numbers did not exist. The earliest counting device was the human hand and its fingers, capable of counting up to 10 things; toes were also used to count in tropical cultures.
Then, as even larger quantities greater than ten fingers and toes could represent were counted, various natural items like pebbles, sea shells and twigs were used to help keep count. Merchants who traded goods needed a way to keep count inventory of the goods they bought and sold.
Various portable counting devices were invented to keep tallies. The abacus is one of many counting devices invented to help count large numbers. When the Hindu-Arabic number system came into use, abaci were adapted to use place-value counting.
Abaci evolved into electro-mechanical calculators, pocket slide-rules, electronic calculators and now abstract representations of calculators or simulations on smartphones. It is important to distinguish the early abacuses or abaci known as counting boards from the modern abaci. The counting board is a piece of wood, stone or metal with carved grooves or painted lines between which beads, pebbles or metal discs were moved.
The abacus is a device, usually of wood romans made them out of metal and they are made of plastic in modern times , having a frame that holds rods with freely-sliding beads mounted on them. Both the abacus and the counting board are mechanical aids used for counting; they are not calculators in the sense we use the word today.
The person operating the abacus performs calculations in their head and uses the abacus as a physical aid to keep track of the sums, the carrys, etc. Educated guesses can be made about the construction of counting boards based on early writings of Plutarch and others. Used 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 the lines would represent the units 10s, s, etc.
Affluent merchants 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. With the need for portable devices, wooden boards with grooves carved into the surface were then created and wooden markers small discs were used as place-holders. The wooden boards then gave way to even more more durable materials like marble and metal bronze used with stone or metal markers. This time-line above click to enlarge shows the evolution from the earliest counting board to the present day abacus.
The introduction of the Arabic numbering system in Western Europe stopped further development of counting boards. Compare the quick rate of progress in last one-thousand years to the slow progress during the first one-thousand years of civilization.
It is a slab of white marble measuring cm in length, 75cm in width and 4. In the center of the tablet are a set of 5 horizontal parallel lines divided equally by a perpendicular vertical line, capped with a semi-circle at the intersection of the bottom-most horizontal line and the 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.
Three sets of Greek symbols numbers from the acrophonic system are arranged along the left, right and bottom edges of the tablet.
During Greek and Roman times, counting boards, like the Roman hand-abacus , that survive are constructed from stone and metal as a point of reference, the Roman empire fell circa C. For the problem 34 x [8] X Research source First, multiply 3 and 1, recording their product in the first answer column.
Push three beads up in that seventh column. Next, multiply the 3 and the 2, recording their product in the eighth column. Push one bead from the upper section down, and one bead from the lower section up.
When you multiply the 4 and the 1, add that product 4 to the eighth column, the second of the answer columns. Since you're adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column four beads from the bottom section pushed up to center bar and a 0 in the eighth all beads in their original starting position: the top section bead pushed up, bottom section beads pushed down.
Record the product of the last two digits 4 and 2 8 , in the last of the answer columns. They should now read 4, blank, and 8, making your answer Part 4. Leave space for your answer to the right of the divisor and the dividend. When dividing on an abacus, you will put the divisor in the left-most column s. Leave a couple blank columns to the right, then put the dividend in the columns next to those.
The remaining columns to the right will be used to do the work leading to the answer. Leave those blank for now. Leave the other columns blank for the answer section. To do this, push two lower beads from the bottom portion up in the left-most column. Leave the next two columns alone. In the fourth column, push three beads from the bottom portion up. In the fifth column from the left, push four beads from the bottom portion up.
The blank columns between the divisor and the dividend are just to visually separate the numbers so you don't lose track of what's what.
Record the quotient. Divide the first number in the dividend 3 by the divisor 2 , and put it in the first blank column in the answer section. Two goes into 3 once, so record a 1 there. To do this, push one bead from the bottom portion up in the first column of the answer section.
If you like, you can skip a column leave it blank between the dividend and the columns you want to use for the answer section. This can help you distinguish between the dividend and the work you do as you calculate.
Determine the remainder. Next, you need to multiply the quotient in the first answer section column 1 by the dividend in column one 2 to determine the remainder. This product 2 needs to be subtracted from the first column of the dividend. The dividend should now read To make the dividend read 14, push two of the bottom portion beads currently pushed up to the center bar at the fifth column back down to their starting position.
Only one bead in the lower portion of the fifth column should remain pushed up to the center bar. Repeat the process. Record the next digit of the quotient in the next blank column of the answer section, subtracting the product from the dividend here, eliminating it.
Your board should now read 2, followed by blank columns, then 1, 7, showing your divisor and the quotient, Two beads from the bottom portion of the left most column will be pushed up to the center bar.
This will be followed by several blank columns. One bead from the bottom portion of the first answer section column will be pushed to the center bar. In the next answer section column, two beads from the bottom portion will be pushed up to the center bar, and the bead from the top portion will be pushed down to it.
Yes, an abacus is a great tool for teaching children basic math. The different senses involved in using an abacus, like sight and touch, can also help reinforce the lessons.
Not Helpful 15 Helpful The type of abacus most commonly used today was invented in China around the 2nd century B. However, abacus-like devices are first attested from ancient Mesopotamia around B. Not Helpful 5 Helpful Your abacus is a Chinese abacus. It has more calculative ability than a Japanese Soroban abacus.
However, the essentials are effectively the same, so these instructions should still work. Not Helpful 26 Helpful My abacus has five beads in the bottom rows. Was it built incorrectly? It says "made in People's Republic of China". As with the last answer to this question, your abacus is a Chinese abacus called suan pan. It has five beads in the bottom row and two in the upper. This page shows instructions for the Japanese abacus called soroban.
Not Helpful 27 Helpful The number of columns can be whatever you want it to be. The important part is the number of beads per column. Not Helpful 24 Helpful Pehaps the Soroban one because it has less beads than a Suan Pan, and also it's the most familiar one. Columns represent digits in a number. An abacus with one column can represent Two columns can represent Three can represent , and so on.
0コメント