ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

The 5 Earth Bead Advantage

The Chinese 2/5 bead suan pan and the 1/5 bead soroban are still in use but as a new generation of students learn on modern streamlined 1/4 bead instruments the numbers of those using these more traditional counting frames are dwindling.

This interesting look at the advantages of using an abacus with 5 earth beads came as a result of a post to the Yahoo Soroban/ Abacus Group by member Hannu Hinkka. Hannu has become our resident expert on Chinese suan pan techniques.

It's well known that the 1/4 bead abacus is a very effective tool. But as it turns out in some instances the extra earth bead on an older style 1/5 soroban or on a traditional 2/5 bead suan pan can make an abacus even more efficient.

Lets look at the example that Hannu gives us in his post to the group. He suggests the subtraction example 644 - 95 = 549. On a 1/4 soroban the operation takes 6 moves and works like this.

Example: 644 - 95 = 549 on a 1/4 soroban (taking 6 moves)

Step 1: Set 644 onto the soroban

Fig.2
  
Step 2
A B C
    .
6 4 4             

Use complementary numbers to solve the problem and count each bead movement. For those familiar with subtraction techniques on a 1/4 soroban, each bead movement is easy to count.

Step 2: Borrow one earth bead from rod F (first move)

Fig.2
  
Step 2
A B C
    .
5 4 4  (1st move)


Step 3: Add one heaven bead to rod G  (second move)

  Fig.3
  
Step 3
A B C
    .
5 9 4  (2nd move)


Step 4: Clear the four earth beads from rod G (third move)

  Fig.4
  
Step 4
A B C
    .
5 5 4  (3rd move)


Step 5:
Clear the heaven bead on rod G (fourth move)

Fig.5
  
Step 5
A B C
    .
5 0 4  (4th move)


Step 6: Add four earth beads to rod G (fifth move)

Fig.6
  
Step 6
A B C
    .
5 4 4  (5th move)


Step 7: Add one heaven bead to rod H (sixth move)

Fig.7
  
Step 7
A B C
    .
5 4 9  (6th move)

And there you have it. After 6 moves we have the answer 549 on rods FGH


This is where Hannu points out the advantage in using an abacus with 5 earth beads. He shows us the subtraction can be done more efficiently in only 4 moves. To illustrate his example I'll use a 1/5 soroban but a 2/5 suan pan would perform just as well. This time the operation will only take 4 moves.

Example: 644 - 95 = 549 on a 2/5 soroban (taking 4 moves)

Step 1a: Set 644 onto the suan pan

Fig.1a
  
Step 1a
A B C
    .
6 4 4          

Step 2a: Borrow one earth bead from rod F (first move)

Fig.2a
  
Step 2a
A B C
    .
5 4 4  (1st move)

Step 3a: Add one earth bead to rod G (second move)

Fig.3a
  
Step 3a
A B C
    .
5 5 4  (2nd move)

Step 4a: Borrow one earth bead from rod G (third move)

Fig.4a
  
Step 4a
A B C
    .
5 4 4  (3rd move)

Step 5a: Add one heaven bead to rod H (fourth move)

Fig.5a
  
Step 5a
A B C
    .
5 4 9  (4th move)

Four moves later we have the answer 549 on rods FGH
 

Hannu concludes his tutorial with the following: "Examples 611-67=544 and 4034-89=3945 have the same sort of situation where the fifth earth bead makes calculation comfortable. Such examples are easy to find."
 
REFERENCES:
Hannu Hinkka
Post # 6770 Yahoo Soroban/Abacus News Group

 

Abacus: Mystery of the Bead
Advanced Abacus Techniques
December, 2011
Totton Heffelfinger   Toronto Ontario  Canada
Email
totton[at]idirect[dot]com