Chapter III: Unusual Properties of Space Summary and Analysis

Dimensions and Co-ordinates

Everyone can conjure up an image of space but what does the word actually mean. It could be termed as that which surrounds us. It could be further defined by referring to the three directions it contains. In a three-dimensional world, we can move forward or back, up and or down and right or left. Coordinates can pinpoint a destination within a space. It is difficult for man to conceptualize superspaces in which there are more than three dimensions. It is easier for man to think in terms of subspaces in which there are less than three dimensions, i.e., two dimensional surfaces and one-dimensional lines.

Geometry without Measure

Ordinary geometry involves the numerical relationship between distances and angles. However, the fundamental property of space does not require...