Note that dimension of a “circle” in a space has to be one less than a dimension of the space. If you get stuck ask for a hint. Draw S1. What are horizontal layers of it? Draw them, and describe them in words. Draw S2. What are horizontal layers of it? Draw them, and describe them in words. What will be horizontal layers of S3. How can one-dimensional person visualize an S1? Circle has to fit into the line! How would a flatlander imagine a sphere, S2? It has to fit onto the plane! How would you imagine a hypersphere?
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