He wrote a treatise on the use of the abacus called Regulae Abaci, which was likely written very early in his career because it shows no trace of Arab influence.

The capital in San Vitale, Ravenna ( 547 ) shows above it the dosseret required to carry the arch, the springing of which was much wider than the abacus of the capital.

The binary abacus is used to explain how computers manipulate numbers.

Depending on how broadly one defines both wearable and computer, the first wearable computer could be as early as the first abacus on a string, or, later, a 16th century pocket watch.

The type of abacus shown here is often used to represent numbers without the use of place value.

* An abacus was created sometime between 1000 BC and 500 BC, it later become a form of calculation frequency, nowadays it can be used as a very advanced, yet basic digital calculator that uses beads on rows to represent numbers.

Before numbers were even invented, counting devices were used to perform everyday calculations ; one of these devices was the abacus, which provided merchants good and accurate data when buying and selling goods.

In the ancient times, the abacus was a really simple device that was used to count numbers ; this included addition and substraction only.

The newest know abacus invented by Lee Kai-chen contains four decks, in which more complex operations can be made ; " multiplication and division are easier using this modified abacus and includes instructions for determining square roots and cubic roots of numbers " ( Georges ).

Napier's bones is an abacus created by John Napier for calculation of products and quotients of numbers that was based on Arab mathematics and lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab and Fibonacci writing in the Liber Abaci.

It is possible to carry out limited arithmetic in base 5 on numbers up to 30 ( decimal ) using your fingers as a rudimentary abacus.

The abacus teaches mathematical skills that can never be replaced with talking calculators and is an important learning tool for blind students.

A person can calculate division with an abacus by repeatedly placing the dividend on the abacus, and then subtracting the divisor the offset of each digit in the result, counting the number of divisions possible at each offset.

In the abacus the combinations are inscribed each on a single slip of wood or similar substance, which is moved by a key ; incompatible combinations can thus be mechanically removed at will, in accordance with any given series of premises.

The Chinese abacus uses two upper beads to represent the 5s and 5 lower beads to represent the 1s, the 7 beads can represent from a hexadecimal digit from 0 to 15 in each column.

The standard abacus can be used to perform addition, subtraction, division, and multiplication ; the abacus can also be used to extract square-roots and cubic roots.

The bead sort operation can be compared to the manner in which beads slide on parallel poles, such as on an abacus.

With counting rods or abacus to perform arithmetic operations, the writing of the starting, intermediate and final values of a calculation could easily be done with a simple additive system in each position or column.

Although electronic calculators have largely replaced the abacus, the latter continues to be used in Japan and other Asian countries.

The upper slots contained a single bead while the lower slots contained four beads, the only exceptions being the two rightmost columns, column 2 marked Ө and column 3 with three symbols down the side of a single slot or beside three separate slots with Ɛ, 3 or S or a symbol like the £ sign but without the horizontal bar beside the top slot, a backwards C beside the middle slot and a 2 symbol beside the bottom slot, depending on the example abacus and the source which could be Friedlein, Menninger or Ifrah.

The Galley method is thought to be of Arab origin and is most effective when used on a sand abacus.

The abacus was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere.

The period 2700 – 2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.

This Mesoamerican abacus used a 5-digit base-20 system.

It consisted of a single cylinder and 22 gears, and employed the mixed base-2 and base-5 number system familiar to users to the soroban ( Japanese abacus ).

* 1003 – Pope Sylvester II, born Gerbert d ' Aurillac, dies ; however, his teaching continued to influence those of the 11th century ; his works included a book on arithmetic, a study of the Hindu-Arabic numeral system, a hydraulic-powered organ, the reintroduction of the abacus to Europe, and a possible treatise on the astrolabe that was edited by Hermann of Reichenau five decades later.

The Babylonians, who were famous for their astronomical observations and calculations ( aided by their invention of the abacus ), used a sexagesimal ( base-60 ) positional numeral system inherited from the Sumerian and also Akkadian civilizations.

This system largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude and in some cases required a device such as an abacus.

The abacus uses a completely graphical system for creating calculations.

The " abacus system " of mental calculation is a system where users mentally visualize an abacus to do calculations.

Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.

Hindu texts used the term shunya ( zero ) to indicate the empty column on the abacus.

This was a finger abacus, on one hand 0 1, 2, 3, and 4 were used ; and on the other hand used 0, 1, 2 and 3 were used.

The Russian abacus, the schoty ( счёты ), usually has a single slanted deck, with ten beads on each wire ( except one wire which has four beads, for quarter-ruble fractions.

The first solid state electronic calculator was created in the 1960s, building on the extensive history of tools such as the abacus, developed around 2000 BC ; and the mechanical calculator, developed in the 17th century.

Suanpan ( the number represented on this abacus is 6, 302, 715, 408 )

For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot.

In their original Greek version, Doric columns stood directly on the flat pavement ( the stylobate ) of a temple without a base ; their vertical shafts were fluted with 20 parallel concave grooves ; and they were topped by a smooth capital that flared from the column to meet a square abacus at the intersection with the horizontal beam ( entablature ) that they carried.

The most recent form know of the logical abacus is a frame made often out of wood which holds firmly a set various rods or wires with freely sliding beads mounted on them ( Georges ).

Nowadays, the abacus still keeps its essence of the frame with rods and beads moving freely on the rods, but is much more developed.

Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.

* Subtraction on a Japanese abacus selected from Abacus: Mystery of the Bead

In the original Sarnath capital ( which is currently situated in Varanasi, Uttar Pradesh ) there are four Asiatic lions standing back to back-symbolizing power, courage, pride, and confidence-mounted on a circular abacus.

The wheel appears in relief in the centre of the abacus, with a bull on the right and a galloping horse on the left, and outlines of Dharma Chakras on the extreme right and left.