Talk:Hyperbolic angle

message: The current image hyperboolhoek.svg is inappropriate for the article text which requires rays to (1,1) and (x,1/x) from the origin. I have placed a request for a similar diagram on hyperbolic sector. A good graphic will help show the unbounded nature of the hyperbolic angle in the first quadrant, an important distinction from the circular case. The current graphic is not so much wrong as it is inappropriate for the development of the concept of hyperbolic angle from fundamentals such as reference to the harmonic series.Rgdboer 23:34, 3 August 2007 (UTC)
replies: text: Thanks to User:Rocchini the is now an appropriate image for this article and hyperbolic sector.Today I changed images to the more appropriate.Rgdboer 22:19, 13 September 2007 (UTC)
thread_title: Image

message: Today I included a 1912 reference to Kennelly's book on application of hyperbolic functions in electrical engineering. Chapter I of this book is "Angles in circular and hyperbolic trigonometry". The approach includes one based on area of a hyperbolic sector. Kennelly's text is flawed by a wrong equation for the hyperbola: yy - xx = 1 instead of xx - yy = 1, a flaw corrected on the page by a reader of the U Cal text digitized. On page 22 he comes to the point of saying that "Θ will be, in hyperbolic radians, double the sector area AOE in sq cm" on his definitive figure. Doubling the area is not necessary when one uses the hyperbola y = 1/x as in the article. On page 25 Kennelly defines hyperbolic sine by XE and hyperbolic cosine by 0X in his figure, similar to statements in hyperbolic triangle. An attentive student will see that XE and 0X give sinh and cosh for half the angle represented in Kennelly's figures. Thus we justly use in WP the hyperbola xy = 1 to establish hyperbolic angle and functions. The faults in Kennelly's text have been weighed against the significance of this reference in history and as a demonstration of the method of acquiring the ideas.
:Rgdboer (talk) 23:34, 17 April 2009 (UTC)
thread_title:  Kennelly 

message: Since Hermann Minkowski wrote Geometrie der Zahlen he is credited with the Geometry of numbers. It is inappropriate to redirect Minkowski geometry to Minkowski space because this relativity article does not pertain to the usual understanding of Minkowski's work in geometry. The change today to Non-Euclidean geometry provides an accurate alternative.Rgdboer (talk) 01:24, 14 November 2009 (UTC)
thread_title:  Geometry name 

message: There might be a mistake in the diagram of circular and hyperbolic angle: File:Circular and hyperbolic angle.svg.
There are two angles in the diagram. One is the hyperbolic angle related to the hyperbola xy=1, and let's call this hyperbolic angle u_hyp. The other is the circular angle related to the circle xx+yy=2, and let's call this circular angle u_cir. Right now in this diagram, these two angles are shown to be indentical, i.e. u_hyp=u_cir=u. I think such indentity should not exit in general, i.e. u_hyp is usually not equal to u_cir. By equations, u_hyp=ArcTanh[Tan[u_cir]]>=u_cir, and u_cir=ArcTan[Tanh[u_hyp]]<=u_hyp, where the equals sign holds only when u_hyp=u_cir=0. In other words, u_hyp is equal to the area of the yellow and red regions, while u_cir is equal to the area of yellow region only.
Armeria wiki (talk) 03:19, 9 June 2013 (UTC)
replies: text: I'll check over this, but the sin, cos trace out the circle and sinh and cosh trace out a hyperbola. All the diagram shows is a different orientation of the curves. Do you have a source to support what your'e saying? M∧Ŝc2ħεИτlk 06:53, 9 June 2013 (UTC)
replies: text: No, I don't have a source. This is my own opinion.Armeria wiki (talk) 05:25, 10 June 2013 (UTC)

text: Perhaps you want :File:HyperbolicAnimation.gif restored or made into a SVG static file? M∧Ŝc2ħεИτlk 07:09, 9 June 2013 (UTC)
replies: text: I'd like to distinguish these two angles in the diagram. They are different.Armeria wiki (talk) 05:25, 10 June 2013 (UTC)
replies: text: Which can be done by redrawing :File:HyperbolicAnimation.gif as SVG, I'll do it soon. M∧Ŝc2ħεИτlk 05:52, 11 June 2013 (UTC)
thread_title:  question about the diagram of circular and hyperbolic angle 

message: The current diagrams indicate hyperbolic angle evolves counter-clockwise like circular angle. Can this assertion be confirmed in references? Probably not, since the concept of hyperbolic angle is tied up with logarithm as made clear in the article hyperbolic sector. There the angle evolves in the opposite direction. Another reason for using the opposite orientation to circular angle lies in the application for rapidity where diagrams generally have frames moving to the right. I suggest that the diagrams be altered accordingly.Rgdboer (talk) 19:25, 12 March 2014 (UTC)
thread_title:  Sense of angle 

message: An editor from Alpharetta, Georgia, changed the formula for sinh in from sin(ix). For clarity, note the series:
:\textstyle\sinh x = \sum_{n=0}^\infty\frac{x^{2n+1}}{(2n+1)!}
Now note that sin has the series converted to an alternating series. Note further
:i^{2n + 1} = i (i^{2n}) = i (-1)^n so that the alternating factor is canceled out.Rgdboer (talk) 01:08, 9 November 2014 (UTC)
thread_title:  Sinh from sin( i x ) 

message: Sorry if I'm just confused here, but it seems to me that the text in the lead contradicts the accompanying image. Currently the text of the lead says
:A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to (x, 1/x) where  x > 1....The hyperbolic angle in standard position is considered to be negative when 0 < x < 1.
But in the accompanying image, reproduced here, u is defined over 0 < x < 1, with the caption saying that u is the area and not its negative. Contradiction? Loraof (talk) 14:51, 14 April 2015 (UTC)
replies: text: Thank you for your interest in consistency for the sense of a hyperbolic angle. Since the work of G. de St. Vincent the sense has usually been positive for x > 1. However, some people have noted that this direction is opposite the counter-clockwise sense for circular angles. The issue arises in images. Furthermore, transformation of the axes determining these senses may be simplified to a rotation and dilation if the senses are made to agree. Thus the image used produces a contradiction that you have noted. The issue was raised before in this Talk, but you are the first to remark on it. An image consistent with historic development and hyperbolic sector is preferred.Rgdboer (talk) 19:01, 14 April 2015 (UTC)
thread_title:  Contradiction between lead image and text? 

message: An angle can have two senses according to motion along the bounding curve (circle or hyperbola). As mentioned above, historically the hyperbolic angle has positive sense opposite the direction of circular angle's positive sense. The diagram at the top of the article confounding the topic with two senses has been replaced with a modest diagram without sense. — Rgdboer (talk) 01:22, 12 March 2019 (UTC)
thread_title:  Sense 

message: As seen in the section Definition, standard position refers to an angle with one side on the line y=x. Using the phrase "standard position" in the lead to mean the hyperbola xy=1, is misleading.  Therefore a change has been made to remove this phrase from the lead of the article. As for confusion with the unit hyperbola xx-yy=1, this article provides an introduction to the argument of hyperbolic functions, and leaves for later development the description of the unit hyperbola as a parametric curve depending on hyperbolic functions. Thank you for your interest in clarifying this topic. — Rgdboer (talk) 01:13, 14 September 2019 (UTC)
thread_title:  Standard position