Famous Theorems
Morley's trisector theorem states that, in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.
Napoleon's theorem states that, if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those equilateral triangles themselves form an equilateral triangle.
A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.
Viviani's theorem states that, for any interior point P in an equilateral triangle, with distances d, e, and f from the sides, d + e + f = the altitude of the triangle, independent of the location of P.
Pompeiu's theorem states that, if P is an arbitrary point in an equilateral triangle ABC, then there exists a triangle with sides of length PA, PB, and PC.
Read more about this topic: Equilateral Triangle
Famous quotes containing the word famous:
“Lizzie Borden took an axe
And gave her mother forty whacks;
When she saw what she had done,
She gave her father forty-one.”
—Anonymous. Late 19th century ballad.
The quatrain refers to the famous case of Lizzie Borden, tried for the murder of her father and stepmother on Aug. 4, 1892, in Fall River, Massachusetts. Though she was found innocent, there were many who contested the verdict, occasioning a prodigious output of articles and books, including, most recently, Frank Spiering’s Lizzie (1985)