# Talk:Unit disk

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)

## 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)

## 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'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)

## 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)

## 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)

## Inverse function

The article states that ${\displaystyle f(z)={\frac {z}{1-|z|^{2}}}}$ is bijective, although Wolfram gives two solutions. Either the statement is false, or the author took a branch of the root. In either case I'm not sure what the policy on Wikipedia (or its math community) is on how to correct such things, as the article obviously should not be bloated. 145.107.16.149 (talk) 08:57, 2 March 2015 (UTC)

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