Talk:Pentagon

Suggestion for improvements

I don't have time at the moment to do this, but this page could use substantial revision. I may try to get to this.

It's really great that people have put a lot of time into this page and that there are several constructions here-- that's what led me here in the first place. But now that they're here, it'd be nice to systemize the presentation and make it more unified.

after all, all the constructions (compass and straightedge constructions, that is) begin in the same way: construct the midpoint and the perpendicular to the given radius. the alternative method and that using the Carlyle circles follow each other for even longer. All the constructions could have, for example, the same notation for the same objects and common steps described in common. There's at least three other constructions that should be included in detail -- Euclid's; a variation where (using the notation of the alternative method) one goes through step 4 of the alternative method, then takes a circle centered on D through point O; two of the five vertices lie on the intersection of this circle with the original and point B is another. Finally, a very nice construction that might or might not be due to John H. Conway and seems the simplest of all: using the notation of the alternative method, go through step 3; take point E to be the intersection of segment AB with the circle centered on midpoint C passing through O and B. Now take the circle centered on A passing through E-- presto! The intersection of this circle with the original gives two vertices.

A construction of penta, given an edge would also be nice to include.

Additional comments: the proof given is kinda beside the point. A purely synthetic proof would be more in the spirit of compass and straightedge, and would be simpler and much less intimidating to some people. All of these constructions set up a golden section and then plop it around; all that's needed is that the golden section appears in the penta as advertised. There are many simple variations -- Euclid's is great.

The so-called direct method really seems kinda, well, stupid. Certainly not at all of the same spirit as the others.

In any case, nice material, but now that it's here, can be taken to a more professional standard.99.175.93.95 (talk) 20:09, 21 August 2010 (UTC)

the pentagon

Excuse me a minute, but isn't it a bit thick to put the geometrical object pentagon aside for a building bearing its shape? Most people in this world will not associate the word "Pentagon" with a building, even though most USA-citizens probably do.

The thing that is on pentagon (shape) should be moved here, and the things here to pentagon (building). Need opinions about this before I do it.

-- Jörgen Nixdorf

Agreed. I thought the same as soon as I saw it. I was going to rename the articles pentagon and The Pentagon. In fact, it seems that articles with those names exist, so your work is half done. -- Heron

There I did it. Nixdorf 07:12 May 13, 2003 (UTC)

• Now begins the real work. Start fixing all these links that now point to the wrong page. -- Minesweeper 08:35 May 14, 2003 (UTC)

I fixed them. All of them. Nixdorf 10:44 May 14, 2003 (UTC)

Did you good:

Whew! Nicely done. -- Minesweeper

---

What is a "no salute, no cover" area? - Montréalais

"Cover" is military jargon for "hat". Normally a US serviceman must salute his superior officers whenever he (the subordinate) is wearing a cover, or is indoors, and must not do so otherwise. Covers are not usually worn indoors. Outdoors, a "no salute, no cover" area is one where you are not required to wear military millinery, and therefore not required to salute your superiors. --Heron

Thanks. If I weren't 10 minutes late for school I'd try to think of a graceful way of putting this into the article. - Montréalais

Done, but not gracefully. --Heron

Disambiguation

I think that there should be a disambiguation for the term "Pentagon". I searched for it, expecting to find results on the building, and was brought to the shape. As Jörgen Nixdorf said, many USA citizens associate this word with the building, and so expect results on the building. But, of course the shape is also an important article. Typing "the pentagon" instead of "pentagon" is something that not a lot of people would consider doing. In short, I think this term needs an disambiguation with links to The Pentagon and Pentagon. I would do it myself, but I don't know how.

Actually, I think if I were going to look for info on the building, I would probably search for "the pentagon", and expect "pentagon" to lead to the shape. Even if not, only one extra click is needed to reach The Pentagon. If there were a disambig, you would need an extra click to arrive at either page, and the article about the shape would need an awkward name like Pentagon (shape). Also bear in mind that the building is named after the shape (I assume). Bistromathic 12:26, 20 August 2007 (UTC)

There is already a Pentagon (disambiguation) page. This article links to it in the intro, and also to The Pentagon for the US government building. It all looks fine to me . -- Steelpillow 21:11, 21 August 2007 (UTC)

Origami pentagon

I thought you might find this interesting: http://www.britishorigami.info/academic/polygons.htm Shinobu (talk) 12:55, 29 September 2008 (UTC)

a pentagon has 5 side —Preceding unsigned comment added by 71.252.187.156 (talk) 22:19, 13 January 2009 (UTC)

Compass as measuring tool

Sorry I don't have time to do more than just mention this:

The "alternative method" described in the article is invalid as a classical contruction method for a pentagon, because it uses a compass as a measuring device.

This is a horribly common method shown for this. In fact the animated gif in this article is one of the very few methods I've seen that actually does it correctly. No wonder our kids are so messed up. :)Kid Bugs (talk) 17:42, 8 February 2009 (UTC)

Could you explain how, please? I'm one of the messed up youths of today, and can't seem to understand which step uses the compass as a measurer! Thanks a bunch! --Oskjoh (talk) 19:11, 1 November 2010 (UTC)

There is no verbal description for the main construction that is illustrated by the GIF. The GIF itself goes by too fast for it to be useful without any verbal description. The first "alternate construction" is a good one, but it has no GIF. The combination is confusing; throughout several visits to the page, I thought the first verbal description (i.e. the first "alternative") was attempting to describe the construction illustrated in the GIF. But the methods are fundamentally different, and I was suffering severe cognitive dissonance watching one construction and reading the description of another.

Could someone write a new description to go with the GIF? 71.255.35.35 (talk) 20:57, 15 December 2009 (UTC)tad brennan

it also had a hidden vertez in it —Preceding unsigned comment added by 208.96.205.10 (talk) 18:15, 23 March 2010 (UTC)

I have finished the "verbal description" as you pleased. (Richmond's Method) I do not understand the "hidden vertez" statement. Which method has the hidden vertex? Bon 062 (talk) 11:25, 29 August 2011 (UTC)

Statement of tiling result

I think the passage "A pentagon cannot appear in any tiling made by regular polygons. To prove a pentagon cannot form a regular tiling, 360 / 108 = 3 1/3, which is not a whole number. More difficult is proving a pentagon cannot be in any tiling made by regular polygons:" needs some work. (1) It's self-contradictory, saying that something is more difficult than itself. (2) The proof, "360 / 108 = 3 1/3, which is not a whole number", leaves out too much detail: why divide by 108 -- and what theorem is being appealed to here? Duoduoduo (talk) 20:06, 24 May 2010 (UTC)

The measure of a pentagon's angle is 108 degrees. Georgia guy (talk) 20:32, 24 May 2010 (UTC)

Right. The statement is self-contradictory. I'll be working on it. Bon 062 (talk) 05:32, 30 August 2011 (UTC)

Yet another construction

I moved the following construction method from the article page, mainly because it was in the wrong section, but also because we already have many construction methods, and this one needs some editing to be in acceptable format. Do we already have more than enough construction methods, or is there value in adding this one?

"Pentagon also can be drawn using general method available with Engineering Drawing Practice. The method involves the following procedure.

• 1.Take side length as t (Let us take t-50mm)
• 2. Draw side length t and call that line as AB
• 3. At B, generate a perpendicular BC such that AB=BC.
• 4. Join C and A.
• 5. Bisect the line AB and generate the line. This line touches line joining C and A at one point. Call it as Point 4.
• 6. Join C and A with an arc with B as Center and AB as radius. This arc cuts the bisecting line at one point. Call it as Point 6.
• 7. Now bisect point 4 and point 6 line to get point 5.
• 8. With Point 5 as center, 5A as radius draw a Circle with Point 5 as center.
• 9. Now start getting Points, by cutting along the circle with B as center get points x, y z with the same approach.
• join ABXYZ to get a pentagon."

Dbfirs 07:48, 3 November 2010 (UTC)

Addition: radius of circumscribed circle (circumradius) and radius of inscribed circle (apothem)

I think these 2 values (in relation with the lenght of the regular pentagon's side) should be presented here one after the another like they are presented in the equilateral triangle article. I made the same request at the square article. Bigshotnews 06:02, 16 February 2011 (UTC) — Preceding unsigned comment added by Bigshotnews (talk • contribs)

Draw Pentagon and 5 Point Star Simplest method

To draw a Pentagon and a 5 pointed star using only a ruler and pair of compasses. [1] Decide the diameter (d) of the pentagon and star that you require, then with compasses draw a circle of that diameter of radius R. (R =d/2). [2] Multiply R x 0.309, call the result r. [3] Draw a circle radius r using the same center as the first circle. [4] Pick any point on the circumference of the first circle (A) and draw a line forming a tangent to the smaller circle. Mark (B) as the point where the extension of this tangent passes through the large circle. [5] Now draw another tangent to the smaller circle from point (B), mark the intersection of its extension with the larger circle as point (C). [6] Now draw another tangent to the smaller circle from point (C), mark the intersection of its extension with the larger circle as point (D). [7] Now draw another tangent to the smaller circle from point (D), mark the intersection of its extension with the larger circle as point (E). [8] The extension of a tangent from point (E) to the smaller circle will end at your original point (A). [9] To create a pentagon from the 5 pointed star draw lines linking ABCDE. Ron Neale62.56.51.38 (talk) 11:02, 5 March 2011 (UTC)

... but most mathematical constructions are restricted to a straight edge and compasses. There are even easier methods if you are allowed to make measurements (and yours are only approximate anyway). Dbfirs 22:09, 6 March 2011 (UTC)

I think this is the quickest method if you need to accurately define the size of the your pentagon/star in advance. I can provide the number 0.309 to as many decimal places as you would like. Then as with all other methods iy becomes a matter of how accurately you can draw. To aid accuracy make sure your "tangents" pass through the lines that describe your circle, i.e. they are point tangents- Ron62.56.48.211 (talk) 10:20, 25 March 2011 (UTC)