Talk:Golden triangle (mathematics)

Decagon reference

Just a clarification, but is it not a regular decagon instead of any decagon? User:Budugoo — Preceding unsigned comment added by 117.217.66.103 (talk) 13:31, 16 January 2013 (UTC)

Type 2?

Clark Kimberling, if you want your "Type 2" definition included, you should mention it here, make the reference available to other editors, and let them decide if it's to be included. It is a conflict of interest for you to decide your new definition has a reliable source. Dicklyon 16:05, 13 February 2007 (UTC)

Gnomons and Pentagrams

Might it be worth it to note also that when a pentagram is drawn inside of a regular pentagon (as per how it's supposed to be done) then each side of the outer pentagon forms a golden gnomon with the nearest vertex of the inner pentagon? —Preceding unsigned comment added by 70.253.161.111 (talk) 01:59, 24 April 2009 (UTC) I don't know what you're on about with this "how it's supposed to be done" stuff, it's really just an arbitrary way of talking around the Golden Ratio, it exists independently of regular pentagons, it's just a number that's very easily seen inside a regular pentagon. As far as I'm concerned, the triangles you can make with side ratios of one and Phi, are far more interesting mathematically and geometrically than what they are when limited to a regular pentagon. Think of tilings and puzzles and such! Ahh, but this isn't any argument, it's a talk page and I ought to be speaking less personally.Cvreise (talk) 04:28, 2 June 2010 (UTC)

Golden gnomon

A gnomon

A gnomon (figure) is defined as a plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. So, a gnomon is a polygon composed by 6 line segments whose 3 line segments are parallel each other and other 3 line segments are parallel each other. According to the definition, a golden gnomon is not a gnomon because a golden gnomon is a triangle. So, in my humble opinion, the term golden gnomon is confusing and should not be used.

a golden gnomon and a golden triangle.

In German, a golden triangle is called as a golden triangle of the first kind (Goldenen Dreieck erster Art) and a golden gnomon is called as a golden triangle of the second kind (Goldenen Dreieck zweiter Art). So, I think that it is better to be called a golden gnomon as a golden triangle of the second kind as follows:

a golden triangle of the first kind

the isosceles triangle whose three angles are in 2:2:1 proportion.

a golden triangle of the second kind

the isosceles triangle whose three angles are in 1:1:3 proportion.

In other words, a golden triangle of the first kind is an acute golden triangle and a golden triangle of the second kind is an obtuse golden triangle.--Ttwo (talk) 18:20, 5 July 2013 (UTC)

The definition of a gnomon can be generalized to triangles, so it is not true that a gnomon cannot be a triangle. Also, Mathworld does only consider golden triangles in 2:2:1 proportion, and uses "golden gnomon" for the other kind.

However, I fully agree that the vocabulary is not stable and varies according to the author. IMHO the article should reflect that. --Agatino Catarella (talk) 20:00, 30 December 2014 (UTC)

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Note similar idea

Please note the similar idea found at https://en.wikipedia.org/wiki/Clark_Kimberling#Kimberling's_golden_triangle . I've added this to the see also section, but it probably should be added to the Golden Triangle disambiguation page as well. — Preceding unsigned comment added by 96.40.48.159 (talk) 00:41, 13 January 2020 (UTC)

Odd statement

@David Eppstein: Golden_triangle_(mathematics)#Angles states

“ The golden triangle is uniquely identified as the only triangle to have its three angles in the ratio 1 : 2 : 2 (36°, 72°, 72°). ”

The bold part emphasises an unremarkable fact: the sum of a triangle's angles in Euclidean geometry is always 180°, thus ignoring reflection, any given ratio uniquely defines its angles, if I understand correctly. For instance, 3 : 1 : 4 yields 67.5°, 22.5°, 90°. Should the statement be simplified to

“ The golden triangle has angles in the ratio 1 : 2 : 2 (36°, 72°, 72°). ”

or similar? Thanks, cmɢʟee⎆τaʟκ 01:05, 10 July 2023 (UTC)