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.
V= 8 8-12+8= 2
E = 12 2=2
F = 8