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# Pappus and desargues finite geometries

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Pappus and desargues finite geometries
Brief definitiion and discussion

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### Pappus and desargues finite geometries

1. 1. Pappus of Alexandria (340 A.D.)
2. 2. Pappus’ Theorem If points A,B and C are on one line and A', B' and C' are on another line then the points of intersection of the lines AB' and BA', AC' and CA', and BC' and CB' lie on a common line called the Pappus line of the configuration.
3. 3. Pappus’ Theorem C B A A' If points A,B and C are on one line and A', B' and C' are on another line then the points of intersection of the lines AB' and BA', AC' and CA', and BC' and CB' lie on a common line called the Pappus line of the configuration. B' C'
4. 4. The Pappus’ geometry configuration has 9 points and 9 lines.
5. 5. Girard Desargues (1591 - 1661) Father of Projective Geometry
6. 6. Desargues’ Theorem 1 Two triangles said to be perspective from a point if three lines joining vertices of the triangles meet at a corresponding common point called the center or polar point.
7. 7. Desargues’ Theorem 1 Two triangles said to be perspective from a point if three lines joining vertices of the triangles meet at a corresponding common point called the center or polar point.
8. 8. Desargues’ Theorem 2 Two triangles are said to be perspective from a line if the three points of intersection of corresponding lines all lie on a common line, called the axis.
9. 9. Desargues’ Theorem 2 Two triangles are said to be perspective from a line if the three points of intersection of corresponding lines all lie on a common line, called the axis.
10. 10. Desargues’ Theorem 3 Desargues' theorem states that two triangles are perspective from a point if and only if they are perspective from a line.
11. 11. Desargues’ Theorem 3 Desargues' theorem states that two triangles are perspective from a point if and only if they are perspective from a line.
12. 12. The Desargues’ geometry configuration has 10 points and 10 lines.
13. 13. Prepared and presented by: AMORY RICAFORT BORINGOT