KALK and WKALK: An introduction to Ancient Klingon Mathematics
KALK and WKALK provide a practical interface to the interesting world of ancient Klingon mathematics. Using a stack based base interface, the user can enter numbers, and execute the four basic arithmetic operations.
Ancient Klingon mathematics used a system based on three, with no zero.Compare counting in base ten to Klingon:
Counting:
Base 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Klingon | 1 | 2 | 3 | 11 | 12 | 13 | 21 | 22 | 23 | 31 |
Simple Math operations
Addition:
+ | 1 | 2 | 3 |
1 | 2 | 3 | 11 |
2 | 3 | 11 | 12 |
3 | 11 | 12 | 13 |
Multiplication:
x | 1 | 2 | 3 |
1 | 1 | 2 | 3 |
2 | 2 | 11 | 13 |
3 | 3 | 13 | 23 |
Perform Klingon Math Online!
This form provides online access to the kalk program that can be downloaded below.
Enter Klingon numbers, and operations below to execute the Kalk program online
. : print and pop stack
+ : add two top entries
- : subtract two top entries (second - top)
x : multiply two top entries
/ : divide two top entries (second / top) top = result, second = remainder
cha' : duplicate top entry
tam : swap top entries
legh : view stack
see : view stack in base 10
remember: ancient Klingon numbers only had the digits 1,2,3 and no ZERO. The number NINE is not "30" (3x3 + 0), but 23 (2x3 + 3x1).
(This example will perform (5 x 5) + 11 in Klingon. Before doing the addition, the "see" command will show the stack in base ten. The final "." displays the result, "popping" the top of the stack for display.)
wKalk - a simple program to do Klingon arithmetic, using the 3 based number system.
CLICK HERE TO DOWNLOAD KALK.ZIP
The KALK.ZIP archive includes the console mode KALK.EXE, and the Visual Basic WKALK.EXE shown above. Source for the KALK.EXE binary is also included.