Undefined terms
Geometry must start from a foundation of words that cannot be defined with other words without eventually being circular (as in, what is a point? A dot. What is a dot? A point), because without these we'd have no vocabulary. Geometry starts with three basic undefined terms.
Extrapolation: Dimensions
A dimension is a measure of direction, such as length, width, or height.
0 DimensionsUnmeasurable- you cannot move in any direction (ex. a point)
1 DimensionLength, but no width- you can move forwards and backwards but not side to side (ex. a line)
2 DimensionsLength and width, but no height- you can move forwards, backwards, side to side, but not up and down (ex. a plane)
3 DimensionsLength, width, and height- you can move forwards, backwards, side to side, and up and down (ex. space)
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