Talk:Trigonometry

We're using this page for general discussion of improving Book 1, Book 2 and Book 3.


 * There is also an About This Book page where 'pedagogic policy' for these three books can be refined and explained and discussed on the talk page.

There are no hard and fast rules as to which talk page to use for what - so do what you think works best.

Old Talk

 * Talk:Trigonometry/Archive 1

American or British English? (and consistency)
this section may become a style guide page, if it becomes overly long...

Some language choices (still under discussion):
 * 'right triangle', not 'right-angled triangle'.
 * 'formulas' not 'formulae'.
 * 'color' not 'colour'.
 * 'center' not 'centre'.
 * 'measure of an angle' rather than just 'angle' (when talking about size of an angle).


 * Having a consistent style is good, but I'm reverting Whoop whoop's unilateral changes pending discussion.--Wisden (discuss • contribs) 13:30, 15 January 2011 (UTC)
 * I think we have to say right-angled, with a hyphen because it is a compound word; "right angled triangle" would include two adjectives, hance mean a triangle that is right and that is angled. A "right triangle" is wrong, because we mean a triangle with a right angle, not a triangle that is right.  "Formulae" is a valid plural of "formula" according to Webster's 3rd New International Dictionary, which I believe is American.  However, if there is a clear consensus for spelling changes, I will agree.--Wisden (discuss • contribs) 13:39, 15 January 2011 (UTC)


 * You were looking in the international dictionary. American English isn't really international.  I always thought "formulae" was the British English version, but Americans wouldn't find either to be incorrect (despite my spellchecker complaining as I type this).  Right triangle states that the triangle names are American versus British.  I actually never knew there was a difference in naming or expected a difference would result over a mere triangle.  I'm not a contributor to this book so I don't have an opinion. – Adrignola discuss 15:19, 15 January 2011 (UTC)


 * I always thought British English was overall more accepted worldwide, if we're going to base a decision on that. (Most ESL speakers I know, for instance, learned with BrE.) At other wikis I edit, we generally respect the preference of the original author unless it's a geographically-specific topic (i.e., an article on American history should be written in AmE). Is there any precedent for this at Wikibooks? Tempodivalse 16:22, 15 January 2011 (UTC)


 * As far as I was aware we did that here as well, but that's only for books lacking a style guide. If a book has established a style guide with the consensus of the contributors to the book, that will override all else.  So for future contributors to this book, this thread ought to produce a style guide for Trigonometry as part of its conclusion.  Help:Local manuals of style provides guidance (though it is itself not complete). – Adrignola discuss 17:55, 15 January 2011 (UTC)


 * +1 on reverting changes pending discussion. If there were an overarching wikibooks preference for BrE or AmE I would go with that.  The book is currently mostly AmE, though changing to either consistently AmE or BrE would be easy.  It actually does not matter if we don't decide this issue right now.  More important to me is that some of the 25% complete pages reach 100% than that we reach a consensus on this topic in a timely manner.  --JamesCrook (discuss • contribs) 19:41, 15 January 2011 (UTC)


 * I agree, and I think since it's currently mostly in American English, it should just be altered to read entirely in American English. Just saying. --Whoop whoop pull up Bitching Betty 21:59, 15 January 2011 (UTC)


 * Also think the current English Wikibooks should become the American English Wikibooks, and we can start up a second British English Wikibooks later. There's a choice between American and British English on Rosetta Stone, why not on Wikibooks as well? --Whoop whoop pull up Bitching Betty 19:30, 22 February 2011 (UTC)


 * That worked out well for Simple English Wikibooks. – Adrignola discuss 19:33, 22 February 2011 (UTC)


 * I assume that's ironic as apparently Simple English Wikibooks is being closed down.--Wisden (discuss • contribs) 21:07, 22 February 2011 (UTC)


 * Indeed. They will not approve any new wikis catering to specific dialects of English and forking the content would lead to one or both of them being closed down due to low participation. – Adrignola discuss 21:27, 22 February 2011 (UTC)

Structure in terms of 3 Books

 * I'd like to keep the contents page all-on-one page for now, until we're approaching featured status for Book 1. Then split, but without page renaming for the book 2 and book 3 component pages (it isn't needed). --JamesCrook (talk) 14:06, 23 December 2010 (UTC)
 * Sounds sensible.--Wisden (talk) 20:30, 24 December 2010 (UTC)
 * As I see it is important to progress sections of this to featured status as they become ready, and that entails subdivision into books - not the only reason for separate books. My current thinking is that we go for featured status for Book 1 without the enthusiasts section, then later for the enthusiasts section, then merge it so that the contents page is all in one for those two books.  We won't merge books 1, 2 and 3, but will provide links between them as they are three volumes from the same 'series'. --JamesCrook (talk) 21:59, 8 January 2011 (UTC)

Scrap Heap Challenge

 * I am thinking at some future date of creating a scrap heap challenge page, and moving all the 'scrap heap' page links there. Whilst we might delete the current crop of scrap-heap pages, I feel there will always be some pages that are on the way out or need rethinking, and going forward don't want to list them all on the front page of the book.  Not a priority to decide at this juncture, just a plan for the future.  --JamesCrook (discuss • contribs) 12:45, 6 February 2011 (UTC)

Maths Notation
--JamesCrook (talk) 14:06, 23 December 2010 (UTC)
 * Using \displaystyle in maths in running text helps to keep the symbols the same in running text and in line-by-line maths, and I think that is helpful and worth doing.
 * We're not yet using the 'German' style of showing the next step to the right. I think that would help, but it will be quite a lot of work making those changes.


 * I think the best way to use this style is if someone who has technical skills in this can create a template for us to use, perhaps calling it "German Math," which allows text to be displayed next to equations without having to work too hard in formatting the page in general? Musical Inquisit (discuss • contribs) 09:29, 25 March 2020 (UTC)

Khan Academy Inspired
These could tie in with Khan Academy:
 * I think a section on chasing-angles would be good to add, after angles sum to 180 degrees. --JamesCrook (talk) 14:06, 23 December 2010 (UTC) Has place holder.
 * I'm tempted to add the Ferris Wheel example as a worked example. --JamesCrook (talk) 14:06, 23 December 2010 (UTC) Done.

=Possible New Topics=

Hesitant to add these as they will delay progress towards featured status.

Possible New Topics: Book 1 2 and 3
Add
 * To Dig Deeper - a page in each book with links mostly to wikipedia. For each topic we will say something about it, about one paragraph.

Perhaps we do that if we have more ideas for new pages than we have time to write them in.

Main Section

 * Triangular numbers. So elementary and also very useful.  Not strictly trigonometry.
 * Vote down, because it is no way related to trigonometry Lightest (discuss • contribs) 18:00, 20 August 2013 (UTC)
 * Polar coordinates.

Enthusiasts Section

 * 'Steiner–Lehmus theorem' (figure on right). Walk through the proof of this.
 * Puzzle: Dividing an equilateral triangle up into n equilateral triangles for n=4,6,8,10....
 * Polar plot of $$\displaystyle r=\cos\theta$$, and other famous or interesting curves like the "heart"
 * Nyquist Frequency. Only going as far as showing that two sine waves can have the same values (at regularly spaced intervals) but be different frequencies....  Relate it to the stroboscopic effect where a wagon wheel is seen as going backwards.

Enthusiasts Section

 * Conway triangle notation. Give alternative proof of Heron's formula.  Show how it reduces the amount of writing especially in triangle-centre proofs.
 * Trilinear coordinate. Usueful for proving results about triangle centres, and in many ways related to conway triangle notation.
 * One-seventh area triangle

Main Section

 * Series definition of Sine and Cosine
 * Proofs of properties under this alternative definition (e.g. periododicity, cf. Rudin's real analysis)
 * Fourier Series

Enthusiasts Section
=Art=

See Talk:Trigonometry/Art for discussion of new artwork and possible images that are available.

Fourier series theory
I don't know how much we want to cover Fourier series in this book; it might be appropriate to have a separate book if one does not already exist elsewhere. Certainly the page on Nyquist frequency (if it is to be written) should be postponed from the elementary section.--Wisden (talk) 18:49, 8 January 2011 (UTC)


 * See clarification of intention around 'Nyquist Frequency' page. They have all the maths they need for it at that stage, and it is a 'for-enthusiasts' topic. --JamesCrook (talk) 21:59, 8 January 2011 (UTC)
 * Not averse at all to a separate book on Fourier series, taking content out of book 3. Could get featured status for both books sooner.--JamesCrook (talk) 21:59, 8 January 2011 (UTC)

Proofs of Geometric Facts in Book 2
Most of the geometric facts mentioned in Book 2 are given without proof, and there is very little discussion on them. Should we include proofs of these facts? And if so, what kind of proofs? Would we strive to only use proofs that include trigonometry, or would any old proof do? Also, would we do multiple proofs of one fact? --Oneequalstwo (discuss • contribs) 14:57, 26 December 2011 (UTC)


 * If you find something does not have a proof associated with it in any part of the book, then go ahead. Also, one does not need to make a proof "using trigonometry." However, if possible, try to use trigonometry within your proof. Also, yes, you can add another proof (as looking at other proofs may be more intuitive than simply one). Musical Inquisit (discuss • contribs) 06:02, 12 June 2020 (UTC)

= Confusing = Hi editors, I appreciate you guys work on compiling the materials. Indeed, the book is something like an invention, especially in book 2 and 3. (Book 1 is cross reference of Khan Academy). There is usually no "Trigonometry" course out of the K-12 curriculum. I know that from older times there is a trigonometry course in undergraduate level, but it seems that we are not referring to that. So the confusing part is: Are we inventing new curriculum for Book 2 and Book 3? If the answer is 'No', where can we find comparable framework in real curriculum? If the answer is 'Yes' (which is more interesting), I am very excited to work with you guys to figure out something new.

For example, Wisden asked if we should cover Fourier series in this book. My answer is definitely yes for the sinusoidal expansion and Bessel's identity, and so on. For the more abstract Hilbert spaces (which belongs to functional analysis) or other orthonormal bases, we should refer the reader to some other books. Lightest (discuss • contribs) 17:56, 20 August 2013 (UTC)