Talk:Unit disk

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Prove that the ratio of the circumference to the diameter of a unit disc is always in between 3 and 4. Hint: These values are attained when the unit disc is a regular hexagon resp. a square (i.e. for the sup norm). — MFH:Talk 14:45, 23 March 2006 (UTC)

Contents 1 Perimeter: Disc or circle? 2 Opaque 3 Golab's theorem? 4 Spelling

[edit] Perimeter: Disc or circle?

I'm not sure the paragraph about the perimeter is relevant to this article. As far as I know, perimeter is a property of the unit circle, and not the unit disc. Maybe you'll add it there instead? -- Meni Rosenfeld (talk) 15:39, 24 March 2006 (UTC)

[edit] Opaque

(was: Area = π?) I smell a rat. John Reid 18:04, 5 April 2006 (UTC)

What seems to be the problem? -- Meni Rosenfeld (talk) 06:53, 6 April 2006 (UTC)

Okay, after the 8th or 9th re-reading, I begin to grasp the topic -- a little. I have had personal experience with the taxicab metric, having once created a map inset graphic defining the limits of the concept "within N blocks".

I retract the rat, but boy, this article is opaque. Needs rewrite for general audience. John Reid 20:19, 7 April 2006 (UTC)

i'm no matematician, nor math student at all, but wasn't the area of a circle πR² ? capi 10:43, 24 April 2006 (UTC)

Yup, it was and is :-) So if the radius is 1, as is the case for the unit disc, you get an area of π. AxelBoldt 20:06, 24 April 2006 (UTC)

[edit] Golab's theorem?

In 1932, S. Gołąb proved that the perimeter of the unit disc can take any value in between 6 and 8

What is the precise statement of this theorem? I can easily give a metric on R² whose unit disc is equal to R² and the perimeter (defined as the unit disc's boundary) is therefore empty. AxelBoldt 19:20, 16 April 2006 (UTC)

I thought I clarified this, but apparently, I did not. According to the article mentioned in the External links section, it should be a metric that arises from a norm. I edited the article to make it at least a bit clearer. Thanks, Jitse Niesen (talk) 06:21, 18 April 2006 (UTC)

[edit] Spelling

Should this article be moved to Unit disk to be consistent with Disk (mathematics)? -- Meni Rosenfeld (talk) 16:31, 28 April 2006 (UTC)

What's the issue here? Is this a British vs. American English thing? AxelBoldt 03:46, 29 April 2006 (UTC)

Yes, Disk (mathematics) uses British (k), and this one, Unit Disc, uses American (c). Not that it matters this much, but I thought it would be good to have them consistent with each other, especially since they link to each other. -- Meni Rosenfeld (talk) 14:42, 29 April 2006 (UTC)

I don't have an opinion on the move, but I can tell you these things go on forever and never settle down. You change it now, in half a year someone else will change it back. AxelBoldt 18:24, 29 April 2006 (UTC)