Modern Geometry

Chuck Friesen, Jul 22, 2014

Most of the GeoGebra files included in this GeoGebraBook were inspired from the reading of these excellent Modern Geometry books: Howard Eves, A Survey of Geometry, Volume One. Boston: Allyn and Bacon, Inc., 1963. Howard Eves, A Survey of Geometry, Volume Two. Boston: Allyn and Bacon, Inc., 1965. Howard Eves, Fundamentals of Geometry. Boston: Allyn and Bacon, Inc., 1969. Howard Eves, Fundamentals of Modern Elementary Geometry. Boston: Jones and Bartlett Publishers, 1992. H. S. M. Coxeter, Projective Geometry. New York: Blaisdell Publishing Co., 1964. H. S. M. Coxeter & S. L. Greitzer, Geometry Revisited. New York: Random House, 1967.


  • 1. Pappus' Theorem
  • 2. Ceva's Theorem

1.

Pappus' Theorem

If the vertices P1, P2, P3, P4, P5, P6 of a hexagon P1P2P3P4P5P6 lie alternately on a pair of lines, then the three intersections E, F, and G of the opposite sides P1P2 and P4P5, P2P3 and P5P6, P3P4 and P6P1 of the hexagon are collinear.

Move any of the six points, P1, P2, P3, P4, P5, P6. What do you notice about points E, F, and G? Is this always true? Are there exceptions?
– Chuck Friesen

2.

Ceva's Theorem

Move E and F (and A, B, C) and observe the ratios of the segments on each side of the triangle.[br]Also observe the product of the three ratios.
1. Position E and F at the midpoints of AC and AB. What do you observe of the ratios?
– Chuck Friesen

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