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Building Blocks of Geometry

Problems

Dimension

Space

Problem : How many dimensions does the following figure have?

One

Problem : How many dimensions does the following figure have?

Two

Problem : How many dimensions does the following figure have?

One

Problem : How many dimensions does the following figure have?

Zero

Problem : How many dimensions does the following figure have?

Two

Problem : If a region in space is spanned by two rays, how many dimensions does it have?

Two

Problem : If a region in space is spanned by an infinite number of points, how many dimensions does it have?

It could have any dimension. The dimension depends on the arrangement of the points. If they are all in a line, then the region is one-dimensional. If the points are noncoplanar, then the region is three-dimensional, etc.

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