Ruler Applications in Geometry
In geometry, a ruler without any marks on it (a straightedge) may be used only for drawing straight lines between points, not measuring. A straightedge is also used to help draw accurate graphs in algebra and other math subjects.
A ruler and compass construction refers to constructions using an unmarked ruler and a compass. It is possible to bisect an angle into two equal parts with ruler and compass. It can be proved, though, that it is impossible to divide an angle into three equal parts using only a compass and straightedge — the problem of angle trisection. However, should two marks be allowed on the ruler, the problem becomes solvable.
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Famous quotes containing the words ruler and/or geometry:
“Despots play their part in the works of thinkers. Fettered words are terrible words. The writer doubles and trebles the power of his writing when a ruler imposes silence on the people. Something emerges from that enforced silence, a mysterious fullness which filters through and becomes steely in the thought. Repression in history leads to conciseness in the historian, and the rocklike hardness of much celebrated prose is due to the tempering of the tyrant.”
—Victor Hugo (1802–1885)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)