Talk:Pythagorean means

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Golden Mean[edit]

hey, is the golden mean thing actually acurate? I'd never heard of more than 3 pythagorean means, but I'm not sure... ROBO (talk) 02:10, 19 November 2007 (UTC)[reply]

Proof[edit]

What is the proof of the graph? Why does it work out so beautifully in a semicircle. I am very curious. 152.2.11.70 (talk) 21:25, 9 February 2009 (UTC)[reply]

I second the request for an explanation of the graph. For one, is it a circle or an ellipse? If it is a circle it seems to be showing the harmonic mean as a radius, which would be equal to A. --Walt (talk) 15:17, 23 October 2009 (UTC)[reply]

Assuming the picture is a semicircle it appears that H > G. 128.40.255.6 (talk) 15:59, 17 May 2010 (UTC)[reply]

I'm quite sure that it's a circle, but I agree that it would be very helpful to see a proof. As for the harmonic mean being too big, you have to look carefully at the colors: the purple for the harmonic mean does not come all the way down to the circle's center; it just comes down to the right angle. Duoduoduo (talk) 18:28, 1 February 2011 (UTC)[reply]

Properties[edit]

The "Value Preservation" property is just a special case of the "Averaging" property. Should it be removed? 24.148.88.178 (talk) 12:58, 24 May 2018 (UTC)[reply]

Domain Restrictions[edit]

The part "Monotonicity and idempotence together imply that a mean of a set always lies between the extremes of the set." is incorrect if the domain is not restricted to postive values for x. For example: take the values -8,-1,1. GM(-8,-1,1) = 8^(1/3) = 2. Max(-8,-1,1) = 1, so GM>Max. Similarly GM(-1,1,8) = -2 < -1 = Min(-1,1,8). 193.10.51.77 (talk) 14:13, 5 July 2023 (UTC)[reply]

(Absolute?) Geometric Mean[edit]

The geometric mean is defined with an absolute value. This is not consistent with the geometric mean page's definition. Is this an assumption of all Pythagorean studies of the GM, a simplification focused on here for certain cases, or something else? 2603:6080:5AF0:9A80:F0B4:82A2:7CB5:9404 (talk) 13:37, 11 October 2023 (UTC)[reply]

In the version history, it looks like the absolute values were added by an anonymous editor on 5 February 2016, so they weren't part of the original article. Note the use of absolute values affects the properties of the function in some important ways, including those noted in the above Domain Restrictions comment. 2603:6080:5AF0:9A80:F0B4:82A2:7CB5:9404 (talk) 13:45, 11 October 2023 (UTC)[reply]