Egyptian multiplication: multiply a×b by repeatedly doubling a and halving b. When b is odd, add the current a to the result. Exactly the same as binary multiplication! Used in ancient Egypt (Rhind Papyrus, ~1650 BCE) and independently in Russia ('Russian peasant multiplication').
How to Use
Enter two numbers:
- Table: Doubling steps
- Selected: Rows where b is odd
- Sum: Final product
Why It Works
Writing b in binary: b = Σ bᵢ·2^i. Then a·b = Σ bᵢ·(a·2^i). The doubling creates a·2^i. The selection (odd b) picks the 1-bits. It's binary multiplication, discovered 3600+ years before binary!
History
Ahmes Papyrus (Rhind Mathematical Papyrus), Egypt ~1650 BCE: earliest known use. Also called 'Russian peasant multiplication' from Russian folk tradition. Ethiopian multiplication is the same algorithm. Shows the universality of binary thinking.
Step-by-Step Instructions
- 1Enter a and b.
- 2Build doubling table.
- 3Mark odd-b rows.
- 4Sum selected rows.
- 5Verify product.