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Leonhard Euler

  • Euler's line is a straight segment created from the circumcenter, centroid, and orthocenter of a triangle

  • The ratio of Euler's line is 1:2
  • He was a Swiss mathematician that made many important discoveries in the area of geometry. The most important of Euler's ideas is the formula for polyhedrons and his line segment. Even when his eyesight deteriorated Euler was able to perform many more discoveries.

Euler's Line

Example

Orthocenter

Euler's Line

Euler's Formulas

Euler's Formula for Polyhedrons

Centroid

  • The formula shows the relationship of the faces, edges, and vertices in a polyhedron.
  • Polyhedron: A closed solid figure that has only flat faces.
  • Formula : V - E+ F = 2

By Diana Ordaz and

Dave Macadaan

Circumcenter

V= # of vertices

E= # of edges

F= # of faces

EXAMPLE

Examples

If the length of Euler's line is 58 cm find the length of the other two parts.

x + 2x = 58

3x = 54

x = 18

Lengths are 18 cm and 36 cm.

5-8+5= 2

2= 2

V= 5

E= 8

F= 5

V= 8 8-12+8= 2

E = 12 2=2

F = 8

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