Background and Problem Statement
Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice the area of a given polygon.
Three problems proved elusive, specifically, trisecting the angle, doubling the cube, and squaring the circle. The problem of angle trisection reads:
Construct an angle equal to one-third of a given arbitrary angle (or divide it into three equal angles), using only two tools:
- an un-marked straightedge and
- a compass.
Read more about this topic: Angle Trisection
Famous quotes containing the words background and, background, problem and/or statement:
“... every experience in life enriches one’s background and should teach valuable lessons.”
—Mary Barnett Gilson (1877–?)
“They were more than hostile. In the first place, I was a south Georgian and I was looked upon as a fiscal conservative, and the Atlanta newspapers quite erroneously, because they didn’t know anything about me or my background here in Plains, decided that I was also a racial conservative.”
—Jimmy Carter (James Earl Carter, Jr.)
“The problem is that we attempt to solve the simplest questions cleverly, thereby rendering them unusually complex. One should seek the simple solution.”
—Anton Pavlovich Chekhov (1860–1904)
“If we do take statements to be the primary bearers of truth, there seems to be a very simple answer to the question, what is it for them to be true: for a statement to be true is for things to be as they are stated to be.”
—J.L. (John Langshaw)