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)
“Silence is the universal refuge, the sequel to all dull discourses and all foolish acts, a balm to our every chagrin, as welcome after satiety as after disappointment; that background which the painter may not daub, be he master or bungler, and which, however awkward a figure we may have made in the foreground, remains ever our inviolable asylum, where no indignity can assail, no personality can disturb us.”
—Henry David Thoreau (1817–1862)
“A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be answered, moveover, in a word—‘Everything.’”
—Willard Van Orman Quine (b. 1908)
“He that writes to himself writes to an eternal public. That statement only is fit to be made public, which you have come at in attempting to satisfy your own curiosity.”
—Ralph Waldo Emerson (1803–1882)