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:
“I had many problems in my conduct of the office being contrasted with President Kennedy’s conduct in the office, with my manner of dealing with things and his manner, with my accent and his accent, with my background and his background. He was a great public hero, and anything I did that someone didn’t approve of, they would always feel that President Kennedy wouldn’t have done that.”
—Lyndon Baines Johnson (1908–1973)
“... every experience in life enriches one’s background and should teach valuable lessons.”
—Mary Barnett Gilson (1877–?)
“I used to be a discipline problem, which caused me embarrassment until I realized that being a discipline problem in a racist society is sometimes an honor.”
—Ishmael Reed (b. 1938)
“He has the common feeling of his profession. He enjoys a statement twice as much if it appears in fine print, and anything that turns up in a footnote ... takes on the character of divine revelation.”
—Margaret Halsey (b. 1910)