El Ábaco

El Ábaco:

Los dispositivos para ayudarnos a contar y calcular aparecieron a medida que se desarrollaban los sistemas numéricos en distintas partes del mundo. Alrededor del año 3,000 a.c., mercaderes y traficantes en el Medio Oriente y a lo largo de la ruta de tráfico del mediterráneo comenzaron a utilizar el ábaco, este simple marco de madera con bolas ensartadas por alambres es aun hoy utilizado en muchas partes del mundo para realizar cálculos contables y comerciales.

Japanese style abacus with bicone beads 1/5 bead soroban from China 1/4 bead soroban by Tomoe

abacus (gif ©ejm) Abacus and Soroban soroban (gif ©ejm)

abacus (gif ©ejm)

abacus (transparent background)

how to use an abacus 

soroban (gif ©ejm)

soroban transparent background)

lee abacus (gif ©ejm)

lee abacus (transparent background)

Lee’s abacus demonstration

abacus (gif ©ejm)     soroban (gif ©ejm)     abacus (gif ©ejm)     soroban (gif ©ejm)     abacus (gif ©ejm)

attempts at making abacus and soroban icons (they don’t really work when they are tiny)

rod 0 - no dot (gif ©ejm)   1 rod 1 - no dot (gif ©ejm)   2 rod 2 - no dot (gif ©ejm)   3 rod 3 - no dot (gif ©ejm)   4 rod 4 - no dot (gif ©ejm)   5 rod 5 - no dot (gif ©ejm)   6 rod 6 - no dot (gif ©ejm)   7 rod 7 - no dot (gif ©ejm)   8 rod 8 - no dot (gif ©ejm)   9 rod 9 - no dot (gif ©ejm) 

rod 0 - dot (gif ©ejm)   1 rod 1 - dot (gif ©ejm)   2 rod 2 - dot (gif ©ejm)   3 rod 3 - dot (gif ©ejm)   4 rod 4 - dot (gif ©ejm)   5 rod 5 - dot (gif ©ejm)   6 rod 6 - dot (gif ©ejm)   7 rod 7 - dot (gif ©ejm)   8 rod 8 - dot (gif ©ejm)   9 rod 9 - dot (gif ©ejm) 

single rods for soroban instruction page (transparent background)

13 reel soroban (gif ©ejm) 

13 reel soroban for abacus instruction page (transparent background)

15 reel soroban (gif ©ejm) 

15 reel soroban for abacus instruction page (transparent background)

soroban (animated gif ©ejm)

soroban gif animation (white background) 

Dilson abacus

Dilson Abacus: This is the abacus that accompanies the Jesse Dilson book. It measures 5.5 inches by 3.5 inches, has 9 columns and is made of a soft wood (possibly white pine) and finished with a glossy transparent laquer. The workmanship is fairly good considering the cost and volume.

Lee abacus standing, oblique view

Lee Abacus:This is the Lee Kai-chen abacus, it measures 13 inches wide and 8 inches high. The design consists of 2 abaci stacked one on top of the other. The top abacus is a 1/4 abacus with 18 columns having small pale green beads on the left half (9 columns) and white beads on the right half (9 columns). The bottom abacus is a 2/5 abacus with 13 columns having larger black beads. Note that the top frame is slightly warped and that the abacus is standing vertically– not a natural position for use (it just photographs better this way).

Lee abacus top-left detail 

Lee Abacus, Detail 1: This is the top-left corner of the Lee abacus.
On the lower abacus, note the white plastic ribbon with red-dots that indicate decimal places. This ribbon slides left-right along the groove between the upper and lower decks via the «roller» (called the «Place Setting Vernier», by the inventor) on the outside of the frame between the two decks of the lower abacus. There is also a decimal place ribbon on the top abacus with green and white markers that slide on the transparent ribbon.

Lee abacus bottom-right detail

Lee Abacus, Detail 2: This is the bottom-left corner of the Lee abacus. Note the corner joint is a simple 45° with a metal re-inforcement nailed to the outside. The decimal place «roller» mounted on the outside of the frame is better visible from this angle.

Tomoe Soroban and box

Tomoe Soroban: The abacus is wrapped in a heavy plastic bag and comes in a box. It has 23 rows; being a Japanese soroban, it is a 1/4 abacus (a single bead in the upper deck and four in the lower deck). It is about 14 inches long and about 2 inches high. This abacus was a gift from the Tomoe Soroban Company.

Tomoe Closeup

Tomoe Soroban Detail: A close-up view of the Tomoe soroban. Every sixth column is marked with a white dot on both the upper and lower frame members. A black dot appears every third column on the beam (the horizontal piece that separates the upper and lower decks).

Three Abaci

Three Abaci: Compare the relative sizes of the Dilson abacus, left, the Tomoe soroban, right-foreground, and the Lee abacus, background.

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