John Wedemeyer, age 14, of Akron, Ohio, for his question:

WHAT IS THE FOURTH DIMENSION?

Most of the time we think of space as having three dimensions: length, width and height. This three dimensional space can easily be seen in a cube. Solid geometry is based on three dimensional space.

But many problems cannot be solved by considering only three dimensions. A problem in designing an airplane, as an example, may require figuring the effect of temperature changes expected at a certain height above sea level at a certain place. Temperature is the fourth dimension in this case.

Algebra is used to solve complicated relationships in geometry since it can be applied to four quantities as easily as to three. Four dimensional geometry has the same relation to solid geometry as solid geometry has to plane geometry.

The language of geometry is used even though a fourth dimension cannot easily be visualized.

Fourth dimension problems are used in the study of all spheres in space. The four dimensions, or quantities, are three distances used to fix the position of the center of the object, and the radius of the sphere.

Time is also often the fourth dimension. Matter, distance and time are too closely related to be separated.

Before an astronomer can know exactly where a star is located, for example, he must know the direction of its travel, its position relative to other stars at different points along its path and also the star's rate of speed.

Time is absolutely necessary to determine all astronomical measurements.

A pilot also uses time to tell his airplane's location on a map. To trace his line of flight on a map, the pilot must multiply his speed per hour by the number of hours in flight. If he has traveled 200 miles an hour for two hours, he knows he is 400 miles along the line.

First to apply mathematics to the geometry of four and more dimensions were two German mathematicians, Hermann Grassman (1809 1877) and Georg Friedrich Riemann (1826 1866).

A third German mathematician, Hermann Minkowski (1864 1909), studied a special case for a point moving in space. The four quantities he used were three distances needed to fix the point of intersection, and the fourth dimension of time.

The three space theory was used later by the great scientist Albert Einstein when he developed his theory of relativity in the early 1900s.