# Is a circle still considered a surface?

1. May 22, 2012

### HAL10000

The question asks to look for a surface and a circle is the only function which meets the conditions. Is this still considered a surface?

2. May 23, 2012

### DonAntonio

If it is really true that only the circle meets the conditions then there's hardly anything to talk about here, but the

interesting thing is, imo: what exactly is your definition of surface?

3. May 23, 2012

### HallsofIvy

Staff Emeritus
No, a circle is a surface if and only if you are talking about the "general" "n dimensional surface" in which case you can think of a circle as a "1 dimensional surface". Of course, it would help a lot if you told what the "question" really is!

4. May 23, 2012

### HAL10000

The question asked for a surface which is equidistant from all points p(x,y,z) to the point (0,0,1) and the plane through z=-1

5. May 23, 2012

### Staff: Mentor

I don't see that a circle figures into this problem at all. In the plane, a parabola is equidistant from a given fixed point and a given line. In other words, at each point P on the parabola, the distance from P to the fixed point is equal to the distance from P to the line.

6. May 23, 2012

### theorem4.5.9

Although a circle is a perfectly good 1 dimensional surface, it's not the solution to your problem.

Find all points $(x,y,z)\in \mathbb{R}^3$ such that
$$\mathrm{distance}\left( (x,y,z) , (0,0,1) \right) = \mathrm{distance}\left( (x,y,z) , \mathrm{plane} \right)$$

I have written it this way as to not give away the answer.

7. May 23, 2012

### HAL10000

Cool :) and I was so certain about that circle lol. Thanks a lot. I get a circular prabolloid with a and b = 2.

Similar Discussions: Is a circle still considered a surface?
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7289231419563293, "perplexity": 543.2988483874523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824293.62/warc/CC-MAIN-20171020173404-20171020193404-00744.warc.gz"}