Compass and Straightedge
Compass and straightedge construction is used to illustrate principles of plane geometry. Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles. The most rigorous definition of this abstract tool is the "collapsing compass"; having drawn a circle from a given point with a given radius, it disappears; it cannot simply be moved to another point and used to draw another circle of equal radius (unlike a real pair of compasses). Euclid showed in his second proposition (Book I of the Elements) that such a collapsing compass could be used to transfer a distance, proving that a collapsing compass could do anything a real compass can do.
Read more about this topic: Compass (drafting)
Famous quotes containing the words compass and and/or compass:
“The statue is then beautiful when it begins to be incomprehensible, when it is passing out of criticism, and can no longer be defined by compass and measuring-wand, but demands an active imagination to go with it, and to say what it is in the act of doing.”
—Ralph Waldo Emerson (1803–1882)
“It is the star to every wand’ring bark,
Whose worth’s unknown, although his height be taken.
Love’s not Time’s fool, though rosy lips and cheeks
Within his bending sickle’s compass come;
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.”
—William Shakespeare (1564–1616)