# Pappus of Alexandria

> 4th century Greek mathematician

**Wikidata**: [Q211783](https://www.wikidata.org/wiki/Q211783)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Pappus_of_Alexandria)  
**Source**: https://4ort.xyz/entity/pappus-of-alexandria

## Summary
Pappus of Alexandria was a 4th-century Greek mathematician and astronomer who made significant contributions to geometry, particularly known for several fundamental theorems that bear his name. Active during the early 4th century CE (circa 300-400 AD), he is considered one of the last major mathematicians of ancient Greece, whose work influenced later developments in mathematics.

## Biography
- **Born:** Unknown date and place
- **Nationality:** Greek (Alexandria, Egypt)
- **Education:** Unknown
- **Known for:** Pappus's centroid theorem, Pappus's hexagon theorem, Pappus' area theorem, Pappus chain, Pappus graph
- **Employer(s):** Unknown
- **Field(s):**
  - Mathematics
  - Astronomy

## Contributions
Pappus of Alexandria authored several important mathematical works that have survived through the centuries. His most notable contributions include:

- **Pappus's Centroid Theorem**: A fundamental theorem in geometry relating the surface area and volume of solids of revolution. It states that for a solid of revolution of a planar figure, the surface area equals the figure's perimeter times the distance the perimeter's centroid travels, and the volume equals the figure's area times the distance the figure's centroid travels.

- **Pappus's Hexagon Theorem**: A classic result in projective geometry stating that if the vertices of a hexagon lie alternately on two lines, then the three pairs of opposite sides meet in three collinear points.

- **Pappus' Area Theorem**: Relates areas of three parallelograms attached to three sides of an arbitrary triangle.

- **Pappus Chain**: A chain of tangent circles within an arbelos, a geometric shape formed by three semicircles.

- **Pappus Graph**: A graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration.

- **Asteroid 29448 Pappos**: An asteroid named in his honor, recognizing his lasting impact on mathematics.

## FAQs
**What is Pappus of Alexandria best known for?**
Pappus of Alexandria is best known for several theorems in geometry, including Pappus's centroid theorem, Pappus's hexagon theorem, and Pappus' area theorem, all of which remain important in mathematical education and research today.

**When did Pappus of Alexandria live?**
Pappus of Alexandria was active during the 4th century CE, with his work period spanning from approximately 300 AD to 400 AD.

**What field did Pappus of Alexandria work in?**
Pappus of Alexandria worked primarily in mathematics and astronomy, though he is most celebrated for his contributions to geometry.

**What is the Pappus graph?**
The Pappus graph is a mathematical graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration, named in honor of Pappus of Alexandria.

**What is the Pappus chain?**
The Pappus chain is a chain of tangent circles within an arbelos, a geometric figure composed of three semicircles, first described by Pappus of Alexandria.

## Why They Matter
Pappus of Alexandria represents one of the final great mathematicians of ancient Greece, bridging classical Greek mathematics and later developments. His theorems remain fundamental in geometry and are still taught in mathematics courses today. The centroid theorem provides a powerful connection between geometric figures and their rotations, while the hexagon theorem is a cornerstone of projective geometry. His work influenced subsequent mathematicians throughout the Islamic world and Renaissance Europe, helping to preserve and transmit Greek mathematical knowledge. Without Pappus's contributions, the historical continuity of mathematical thought from antiquity to the modern era would be significantly diminished.

## Notable For
- Authoring influential mathematical treatises in the 4th century CE
- Developing Pappus's centroid theorem, a fundamental result in geometry
- Creating Pappus's hexagon theorem, essential to projective geometry
- Describing the Pappus chain, important in the study of circle configurations
- Inspiring the naming of asteroid 29448 Pappos
- Being among the last major mathematicians of ancient Greece

## Body

### Historical Context
Pappus of Alexandria lived during the 4th century CE in Alexandria, Egypt, which was then part of the Roman Empire. This period marked the late phase of ancient Greek mathematics, with Pappus being one of the last significant mathematicians before the decline of classical mathematical traditions in the region. Alexandria, as a major intellectual center, provided the environment for his scholarly work.

### Mathematical Contributions
Pappus's work spanned several areas of mathematics, with his most significant contributions being in geometry. His theorems have been studied and applied for over seventeen centuries.

**Pappus's Centroid Theorem**: This theorem establishes two fundamental relationships for solids of revolution. First, it relates the surface area of a solid to the distance traveled by the perimeter's centroid. Second, it connects the volume of a solid to the distance traveled by the figure's centroid. This theorem demonstrates Pappus's sophisticated understanding of geometric relationships and his ability to derive general principles.

**Pappus's Hexagon Theorem**: This projective geometry theorem states that when the vertices of a hexagon alternate between two lines, the three pairs of opposite sides intersect at collinear points. This result has proven fundamental in the development of projective geometry and continues to be taught in advanced mathematics courses.

**Pappus' Area Theorem**: This theorem addresses the relationships between areas of parallelograms constructed on the sides of an arbitrary triangle, demonstrating Pappus's interest in geometric relationships and area calculations.

### Geometric Constructions
Beyond his theorems, Pappus contributed to the understanding of complex geometric configurations. The Pappus chain represents a specific arrangement of tangent circles within an arbelos, a shape formed by three semicircles with collinear centers. This construction has interested mathematicians studying circle configurations and continues to be the subject of geometric investigation.

The Pappus graph, with its 18 vertices and 27 edges, represents the Levi graph of the Pappus configuration. This graph-theoretic representation has applications in the study of geometric configurations and combinatorial mathematics.

### Legacy and Influence
The recognition of Pappus's contributions is evidenced by the naming of asteroid 29448 Pappos after him. This celestial honor reflects the lasting significance of his mathematical work.

Pappus's writings helped preserve Greek mathematical knowledge through the centuries, serving as a bridge between ancient mathematics and later developments in the Islamic world and Renaissance Europe. His works were studied by subsequent generations of mathematicians, contributing to the transmission of mathematical ideas across cultures and time periods.

### Position in Mathematical History
As one of the last major mathematicians of ancient Greece, Pappus represents the culmination of a mathematical tradition that began with figures like Euclid, Archimedes, and Apollonius. His work demonstrates both the continuity of Greek mathematical thought and the sophisticated level of geometric understanding achieved in late antiquity. The theorems that bear his name remain active areas of mathematical study and application, testifying to their fundamental importance in the field.

## References

1. MacTutor History of Mathematics archive
2. Dictionary of African Biography
3. International Standard Name Identifier
4. CiNii Research
5. CERL Thesaurus
6. Virtual International Authority File
7. Catalogue of the Library of the Pontifical University of Saint Thomas Aquinas
8. Freebase Data Dumps. 2013
9. Name and Title Authority File of Catalonia
10. [Source](http://digitale.beic.it/primo_library/libweb/action/search.do?fn=search&vid=BEIC&vl%28freeText0%29=Pappus_Alexandrinus)
11. IdRef
12. CONOR.SI
13. Czech National Authority Database
14. Treccani's Enciclopedia on line
15. Enciclopedia Treccani
16. LIBRIS. 2012
17. HMML Authority File
18. Digital Scriptorium Catalog