Prehistoric Mathematics and Tools

Study Notes

Early humans had a basic understanding of quantity, recognizing "one," "two," and "many."
The concept of abstract symbols for numbers developed over time.
Evidence of early mathematical thinking includes notched bones from Africa dated 20,000-25,000 years old.
Mathematics existed before written records.

A bone artifact from Africa dated to 20,000 BC.
Contains markings that may represent a calendar, a lunar phase counter, or a number system.

Used a system of hieroglyphics for numerals.
Developed a base-10 system with symbols for 1, 10, 100, 1,000, and so on.
Used unit fractions for division.
The Rhind Papyrus is a key source for understanding Egyptian mathematics, written around 1650 BC.
Demonstrates knowledge of arithmetic, geometry, and algebra.
The Eye of Horus Papyrus shows their system of unit fractions, based on the Eye of Horus symbol.
Egyptians approximated the area of a circle by multiplying the diameter by 8/9 and squaring the result.
Constructed the pyramids, showcasing their understanding of geometry and volume calculation.

Fractional notation developed for market and trade needs.
Eye of Horus symbol was used to represent fractions (half, quarter, eighth, sixteenth, thirty-second, sixty-fourth).
Example: Divide 3 loaves between 5 people.
- Each person receives 1/3 + 1/5 + 1/15 = 3/5 of a loaf.

Ahmes: Scribe who copied the Rhind Papyrus, providing valuable insights into Egyptian mathematics.
Abu’l-Hasan Ibn Yunus: Prominent astronomer and mathematician, known for his meticulous calculations and the lunar crater named after him.

Mesopotamia, the "Cradle of Civilization."
The Sumerians developed the oldest known writing system: cuneiform script.
Early development of mathematics for land measurement, taxes, and calendrical calculations.
Used a sexagesimal system (base 60) for their number system.
Developed a place-value system for numbers, unlike other ancient civilizations.

Used symbols for one, ten, and sixty for counting.
Used cuneiform symbols for numerals, written with a stylus.
Had a placeholder symbol functioning like zero.
This system was advantageous for its divisibility by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 60.
Continues to influence our current timekeeping and angle measurements.

Show evidence of their knowledge of geometry and calculation of areas, volumes, and quadratic equations.
The Plimpton 322 tablet suggests possible knowledge of Pythagorean triples (a² + b² = c²), predating Pythagoras.

Developed the place-value system, critical for modern mathematics.
Invented the concept of zero as a placeholder.
Made significant contributions to algebra, geometry, and astronomy.
Laid the foundation for later mathematical advancements in various civilizations.