Number Systems

10.

Historical and Alternative Number Systems

10.1.

Ancient Non-Positional Systems

10.1.1.

10.1.1.1.

Basic Counting Methods

10.1.1.2.

Archaeological Evidence

10.1.1.3.

10.1.2.

10.1.2.1.

10.1.2.2.

Combination Rules

10.1.2.3.

Subtractive Notation

10.1.2.4.

Mathematical Limitations

10.1.3.

Egyptian Hieroglyphic Numerals

10.1.3.1.

10.1.3.2.

Additive Principle

10.1.3.3.

Historical Context

10.2.

Historical Positional Systems

10.2.1.

Babylonian System (Base-60)

10.2.1.1.

Cuneiform Notation

10.2.1.2.

Place Value Structure

10.2.1.3.

Mathematical Achievements

10.2.1.4.

Legacy in Time Measurement

10.2.2.

Mayan System (Base-20)

10.2.2.1.

Vigesimal Structure

10.2.2.2.

10.2.2.3.

Calendar Applications

10.2.2.4.

Mathematical Sophistication

10.2.3.

Chinese Rod Numerals

10.2.3.1.

Positional Notation

10.2.3.2.

Decimal Structure

10.2.3.3.

Historical Development

10.3.

Specialized Number Systems

10.3.1.

Balanced Ternary

10.3.1.1.

Structure and Properties

10.3.1.2.

Computational Applications

10.3.2.

Factorial Number System

10.3.2.1.

Structure and Applications

10.3.2.2.

Permutation Representation

10.3.3.

10.3.3.1.

Zeckendorf Representation

10.3.3.2.

Unique Properties

10.4.

Cultural and Mathematical Impact

10.4.1.

Influence on Modern Mathematics

10.4.2.

Cross-Cultural Exchange

10.4.3.

Evolution of Mathematical Thinking

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9. Character and Data Encoding

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1. Introduction to Number Systems