Dividing A Given Circle Into Four Equal Arcs Given Its Centre
Centred on any point X on circle C, draw an arc through O (the centre of C) which intersects C at points V and Y. Do the same centred on Y through O, intersecting C at X and Z. Note that the segments OV, OX, OY, OZ, VX, XY, YZ have the same length, all distances being equal to the radius of the circle C.
Now draw an arc centred on V which goes through Y and an arc centred on Z which goes through X; call where these two arcs intersect T. Note that the distances VY and XZ are times the radius of the circle C.
Put the compass radius equal to the distance OT ( times the radius of the circle C) and draw an arc centred on Z which intersects the circle C at U and W. UVWZ is a square and the arcs of C UV, VW, WZ, and ZU are each equal to a quarter of the circumference of C.
Read more about this topic: Napoleon's Problem
Famous quotes containing the words dividing, circle, equal and/or centre:
“When a man and a woman have an overwhelming passion for each other, it seems to me, in spite of such obstacles dividing them as parents or husband, that they belong to each other in the name of Nature, and are lovers by Divine right, in spite of human convention or the laws.”
—Sébastien-Roch Nicolas De Chamfort (1741–1794)
“A beauty is not suddenly in a circle. It comes with rapture. A great deal of beauty is rapture. A circle is a necessity. Otherwise you would see no one. We each have our circle.”
—Gertrude Stein (1874–1946)
“The idea of feminine authority is so deeply embedded in the human subconscious that even after all these centuries of father-right the young child instinctively regards the mother as the supreme authority. He looks upon the father as equal with himself, equally subject to the woman’s rule. Children have to be taught to love, honor, and respect the father.”
—Elizabeth Gould Davis (b. 1910)
“Old politicians, like old actors, revive in the limelight. The vacancy which afflicts them in private momentarily lifts when, once more, they feel the eyes of an audience upon them. Their old passion for holding the centre of the stage guides their uncertain footsteps to where the footlights shine, and summons up a wintry smile when the curtain rises.”
—Malcolm Muggeridge (1903–1990)