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Mayan Numbers

Convert between decimal and Mayan vigesimal (base-20) number system with dots, bars, and shells.

Each line = one place. Use . for dots, - for bars, o for shell (zero)

Mayan Numeral Symbols

Dot = 1

Bar = 5

Shell = 0

Examples

How Mayan Numbers Work

  • • Base 20 (vigesimal) number system
  • • Written vertically - highest place at top
  • • Place values: 1, 20, 400 (20²), 8000 (20³)...
  • • Each place can be 0-19 using dots (1s) and bars (5s)

What are Mayan Numbers?

The Maya civilization developed one of the most sophisticated number systems in the ancient world. Using only three symbols - a dot (1), a bar (5), and a shell-like symbol (0) - they could represent any number in their vigesimal (base-20) positional system.

The Symbols

  • Dot (●): Represents 1
  • Bar (▬): Represents 5
  • Shell (⊛): Represents 0 (the Maya invented zero independently!)

How the System Works

Single Digits (0-19)

Numbers 1-19 are represented using combinations of dots and bars:

  • 1-4: One to four dots
  • 5: One bar
  • 6-9: One bar plus one to four dots
  • 10: Two bars
  • 15: Three bars
  • 19: Three bars plus four dots

Place Values

Like our decimal system, Mayan numbers use place values, but in base 20:

  • Bottom position: ×1
  • Second position: ×20
  • Third position: ×400
  • Fourth position: ×8000

Mayan Numbers in Geocaching

These numbers appear in puzzles because:

  • Visual appeal: The symbols make interesting puzzle graphics
  • Historical theme: Archaeology and ancient civilization caches
  • Base-20: Different way of thinking about numbers
  • The zero: The Maya's invention of zero is historically significant

Historical Significance

The Maya were one of only a few cultures to independently discover the concept of zero. Their mathematics was used for astronomical calculations, calendar systems, and architecture. The Long Count calendar used this number system to track dates over thousands of years.

Related Topics

  • Roman Numerals: Another ancient number system.
  • Base Conversion: Converting between number bases.
  • Babylonian Numbers: Another ancient positional system.