In Mathematics
In elementary models of space, height may indicate the third dimension, the other two being length and width. Height is normal to the plane formed by the length and width.
Height is also used as a name for some more abstract definitions. These include:
- The altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
- A measurement in a circular segment of the distance from the midpoint of the arc of the circular segment to the midpoint of the line line joining the endpoints of the arc (see diagram in circular segment);
- In algebraic number theory, a "height function" is a measurement related to the minimal polynomial of an algebraic number;
among other uses in commutative algebra and representation theory.
Read more about this topic: Height
Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)