Talk:Special right triangle

More info, please!

This article is nice, but is very small. On such a broad topic, you'd think that there would be more information available than what is in the article. Perhaps someone could pump it up some? ROBO 04:04, 6 October 2007 (UTC)

There should be more, for example, a simple formula to find the two sides of a 45-45-90 triangle when one knows only the hypotenuse. 198.150.12.32 (talk) 16:09, 24 April 2008 (UTC)

What about the other triad pattern; 3:4:5 5:12:13 13:84:85 85:3612:3613 3613:6526884:6526885 and so on. we've worked out the pattern, but it's not mentioned here. If it's a new discovery email me at boredom-tekno@hotmail.com —Preceding unsigned comment added by 144.134.229.100 (talk) 10:01, 12 June 2008 (UTC)

This should be put under something other than Special Right Trianles "unit circle" would be more apropriate. The discustion of radians is lacking and a full 360 degree of the radians should be listed, from Pi/2 - 2pi.--69.238.168.142 (talk) 23:08, 1 September 2011 (UTC)

Where are the 18-72-90 (π/10,2π/5,π/2 or 1:√(2√5+5):1+√5) and 36-54-90 (π/5,3π/5,π/2 or √(10-2√5):1+√5:4) special triangles? — Preceding unsigned comment added by 75.172.58.83 (talk) 16:03, 1 November 2021 (UTC)

Classification

I don't think the classification of special right triangles as angle based and edge based is very common (e.g. Edge based right triangles are more commonly called Heronian right triangles or Pythagorean triangles, isn't it?). Other special right triangles that fall outside the above two categories exist as well, for instance the Kepler triangle.

All right triangles that can be labeled special have at least one integer edge (or can be scaled such as to have one integer edge). So, perhaps a more suitable classification would be:

• Right triangles with three integer edges (i.e. Heronian right triangles based on Pythagorean triplets, or: primitive right triangles)
• Right triangles with two integer and one non-integer edge (currently referred to as the "angle-based special right triangles)
• Right triangles with one integer edge and two non-integer edges (e.g. Kepler triangle)

Perhaps alternative classifications are also possible? JocK 22:34, 27 October 2007 (UTC)

30-60-90 image

The previous edit removed the 30-60-90 triangle because of "an error". Could you explain what the error is? Simply removing an image that is an integral part of the article is not helpful. --dbolton (talk) 16:52, 24 January 2010 (UTC)

Biased language?

The description of the 30-60-90 triangle contains the following sentence:

The designation 30-60-90 is not only cumbersome, it references the degree, an arbitrary division of angular measure.

While arguments could be (and have been) made regarding the arbitrariness of the degree, this sentence comes off as condescending and dismissive, and this hardly seems the place to bring up that sort of thing. (I notice there's no similar complaint about the 45-45-90 triangle.) Like it or not, degrees ARE a worldwide de facto standard for angular measure, and far more widely recognized in non-scientific discourse than radians. I also don't see how the designation is "cumbersome", compared to the alternatives. (You'd never see a π/6-π/3-π/2 triangle template for sale in your local drafting supply store, for example, or for that matter a 1 : √3 : 2 triangle.) Can we find a better way of wording that, maybe? Lurlock (talk) 17:37, 5 February 2010 (UTC)

Confusion on angle ratios

I cannot see why the angle ratios are stated as their sines which are, of course, the same ratio as their sides. Surely 30°, 60°, 90° angles are in a ratio 1:2:3 not 1:√3:2, and 45°, 45°, 90° angles are in a ratio 1:1:2 not 1:1:√2. I will change these ratio unless there is some explanation. Frank M Jackson (talk) 17:19, 9 August 2010 (UTC)

Amendment now actioned. Frank M Jackson (talk) 07:49, 12 August 2010 (UTC)

Right triangle whose angles are in a geometric progression

This new section added by User:Fjackson is sourced to an integer sequence uploaded by Frank Jackson on Aug. 6 2010. Is this considered a reliable source? Is it peer reviewed? Published? And shouldn't Frank has mentioned it here instead of adding it himself? Dicklyon (talk) 06:06, 21 September 2010 (UTC)

Apologies for not being aware of normal protocol on such a matter. This is a very simple property that can be easily verified and it contributes to the properties of special triangles relating to their angles. Unfortunately a standard web search could not identify any references. The insertion of the integer sequence into OEIS, a well respected reference web site, was to ensure proper peer review. The sequence was reviewed and partially edited by mathar@strw.leidenuniv.nl. If it is still believed that this simple property needs a more thorough peer review please advise preferred method. Use talk page, if appropriate. Frank M Jackson (talk) 19:24, 21 September 2010 (UTC).

I'm not aware of the OEIS being considered peer reviewed. Does it say so some place? It's an OK source for sequences, but for the stuff about special triangle relationships, I don't see how to consider this new stuff as anything more than self-published. We get tons of new results on golden ratio all the time, which is why we firm back firmly to hold the line based on WP:V and WP:RS. Being mathematically verifiable is not sufficient. Get it published first. Dicklyon (talk) 05:13, 22 September 2010 (UTC)

I don't hold strong views on this specific matter, but would like to put forward a few words in support of Fjackson's edits. Simple mathematical relations that can be easily verified don't need references. In this particular case any 15 year old with some math education can verify Fjackson's edits. Let's face it: the no original results guideline is there to prevent crackpot contributions. This particular contribution does not come anywhere near to crackpottery. JocK (talk) 18:29, 22 September 2010 (UTC)

This definition of a new type of unique right triangle is easy to verify mathematically, I agree, but it takes at least a bit of logic to prove uniqueness, so it's not a trivial matter. But in terms of what's worth talking about in wikipedia, it's still original research. Wikipedia:OR#Routine_calculations says "This policy allows routine calculations, such as adding numbers, converting units, or calculating a person's age, provided editors agree that the arithmetic and its application correctly reflect the sources," which doesn't seem to apply here; are you thinking of any other guideline about mathematics? I think he should publish it and get some credit for it, and then we can talk about it here. Otherwise we're setting a bad precedent that will allow the golden ratio page to be bloated with this and every other new factoid than people come up with involving it. Dicklyon (talk) 05:44, 23 September 2010 (UTC)

Angle ratios

I reworded some stuff about angle ratios, into angle relationships; there's a fundamental difference between how these shapes can be specified to side ratios like 3 : 4 : 5, and by angle relationships, like 45-45-90. In the latter, the ratio is 1 : 1 : 2, but that's not enough; add the constraint that it's a right triangle forces the values, unlike the sides, where only the ratio matters. I think the wording was misleading and confusing before.

I also changed all the italicized numbers that I could find to be not italics. Dicklyon (talk) 19:07, 12 February 2011 (UTC)