Napier’s Bones Calculator
A 17th-century mechanical multiplication tool
Calculation Setup
Quick Examples:
Napier’s Bones
Calculation Result
About Napier’s Bones
Invented by John Napier in 1617, this mechanical calculator used numbered rods (“bones”) to simplify multiplication.
How it works: Each bone shows multiples of its digit. To multiply:
- Select bones for the multiplicand’s digits
- Read diagonally for each multiplier digit
- Add diagonally to get the final product
John Napier invented both Napier’s Bones AND logarithms! These two inventions share the same fundamental insight: transforming complex multiplication into simpler operations.
Both systems use pre-computation to speed up calculations. Napier’s Bones was the mechanical precursor to the logarithmic slide rule.
The “diagonal addition” in Napier’s Bones is an early example of diagonalization.
- Cantor’s Diagonal Argument
- Matrix Diagonalization
- Gödel’s Incompleteness
- Turing’s Halting Problem
Napier’s Bones demonstrates space–time tradeoff.
This mirrors:
- CPU caches
- Lookup tables
- Dynamic programming
- Hash indexing
Carry propagation in Napier’s Bones is base-10 modular arithmetic.
7×4=28+4=32 → ones=2, carry=3
This mirrors finite fields, CPU arithmetic, and crypto reductions.