Wikipedia:Graphics Lab/Illustration workshop

Flagge Reichsbanner 2013.jpg|Flag of Reichsbanner Schwarz-Rot-Gold (JPG version)

Flagge Reichsbanner 2013.svg|Flag of Reichsbanner Schwarz-Rot-Gold (SVG version)

Logo Reichsbanner 2013.svg|Logo of Reichsbanner Schwarz-Rot-Gold (use this as a possible base)

Vectorized Reichsbanner Logo.svg|Logo of Reichsbanner Schwarz-Rot-Gold (use this as a possible base)

;Article(s):

: Reichsbanner Schwarz-Rot-Gold, List of German flags

;Request:

: Hi, I was wondering if someone can kindly please vectorize the flag of "Reichsbanner Schwarz-Rot-Gold"? I have included here two versions of the organization's logo to use as a base so the request can be done more quickly. Both version of the logo might need fixing though so please also do that if you vectorize the flag. One part that might be difficult is the Fraktur font for the words on the black and gold stripes. The words in yellow on the black stripe read "Reichsbanner Schwarz-Rot-Gold" and the words in black on the yellow stripe read "Einigkeit und Recht und Freiheit" (meaning "Unity and Justice and Freedom" which is the national motto of Germany and is taken from the German national anthem). Thanks in advance! -- 109.79.104.45 (talk) 22:03, 19 April 2025 (UTC) File:Pictogram voting wait.svg Bumping thread. 109.77.41.191 (talk) 13:00, 17 May 2025 (UTC){{User:ClueBot III/DoNotArchiveUntil|1750078841}} Because I'll be away!--109.77.41.191 (talk) 13:00, 17 May 2025 (UTC)

;Discussion:

File:Coat of arms of the United Kingdom (2024, lesser arms).svg|Current version

;Article(s):

: Several

;Request:

An IP editor came to my page to point out that the current stylization of the UK Coat of Arms as used by HM Government appears to slightly differ in the organization of the motto from the drawing published by HM Government. Could use a fix, but there also might be something I'm missing. -- estar8806 (talk) ★ 18:29, 29 April 2025 (UTC)

:I think it's OK to not use the official color of the motto to avoid copyright issues, but the position of the motto should be similar to the official one. 112.105.122.226 (talk) 18:39, 29 April 2025 (UTC)

::Official reference sources：https://www.gov.uk/government/news/new-coat-of-arms-artwork-unveiled 112.105.122.226 (talk) 18:42, 29 April 2025 (UTC)

:::@Dgp4004 112.105.122.226 (talk) 10:46, 2 May 2025 (UTC)

::::Thank you for the ping, but as I've said several times already, copying minute details from UK Government files is an infringement of Crown Copyright. The file is fine as it is. Several editors have said no to this request already but you persist with a fresh IP address each time. For these reasons and as the file's creator, I am opposed to the changes requested. Dgp4004 (talk) 11:12, 2 May 2025 (UTC)

:::::Would changing the text arrangement in the scroll violate copyright, for example, moving 'ET MON' from the center to the sides like the official version instead of keeping it in the middle? 112.105.122.226 (talk) 15:11, 2 May 2025 (UTC)

::::::My main concern is that in the 2022 version you created, the placement of the text within the scroll seems to follow past versions, which is noticeably different from the current version. Therefore, I'm hoping that at least the text position within the scroll can be adjusted. As for the other parts, they don't necessarily need to be changed. 112.105.122.226 (talk) 15:19, 2 May 2025 (UTC)

:::::Specifically, place 'DIEU ET' on the left side of the scroll, leave the center blank, and place 'MON DROIT' on the right side. Only make this change; do not adjust other aspects like the direction the scroll curves or its color. Would making this change also infringe on copyright? 112.105.122.226 (talk) 15:26, 2 May 2025 (UTC)

::::::I have no control over my IP address because it will change whenever I shut down and reconnect. 112.105.122.226 (talk) 15:38, 2 May 2025 (UTC)

;Discussion:

: I think that in the absence of clear evidence that the ratio of the flag should be close to 5:8, the flag should follow the past ratio of 1:2.

: :File:Royal Standard of Canada.svg

: :File:Royal Standard of members of the Canadian Royal Family.svg

112.105.122.226 (talk) 18:35, 29 April 2025 (UTC)

:: Not to mention that from this picture, the flag ratio does not seem to be 5:8 :File:Sovereign’s Flag for Canada.jpg

:: https://www.canada.ca/en/canadian-heritage/services/royal-symbols-titles/canadian-flags-royal-family.html

:112.105.122.226 (talk) 18:35, 29 April 2025 (UTC)

::The illustration on the Canadian Heraldic Authority's Public Register of Arms, Flags and Badges of Canada is 5:3:

::*[https://www.gg.ca/en/heraldry/public-register/project/3535 Sovereign's Flag for Canada]

::Hogweard (talk) 20:29, 29 April 2025 (UTC)

:::However, I checked and found that all the illustrations above are drawn in the same proportion (including the Queen's flag in the past), but from past situations, it seems that different proportions are used in actual use. The same is true for the Governor's flag shown on other pages. The two pictures I mentioned are indeed inconsistent with the proportions of other existing flags.

:::That’s why I hope the ratio of these two pictures can be consistent with the ratio of other pictures. Most of the pictures I have seen in the past are 1:2. 112.105.122.226 (talk) 08:58, 30 April 2025 (UTC)

::::Is there any mileage in asking the Governor-General's office what are the actual proportions of the cloth flag which His Majesty actually uses? And for a good photograph / graphic? I believe the GG is rather busy at the moment, but maybe after the current flapdoodle has calmed down... Hogweard (talk) 06:44, 1 May 2025 (UTC)

:::::What I mean is that the proportions of the flags shown on the webpage may not be the same as the proportions of the flags actually used. 220.138.86.130 (talk) 12:02, 1 May 2025 (UTC)

::::::That's what I thought you meant, and you are quite right. What we need to find out then is what are the proportions of the flags actually used. I understand that Her Late Majesty used a flag in the same proportions as the national flag, which is to say 2:1, but the illustration provided by the Canadian Heraldic Authority is 5:3. The old Guidance from the College of Arms was that sea flags should be 2:1 and land flags 5:3 but I have not seen that stuck to: the Union Jack and the Flag of Canada are always 2:1 on land and sea, and I think the Royal Standard that flies from Buckingham Palace is 2:1. The UK Flag Institute is dead-set on 5:3 and they have even tried to get the Union Jack changed.

::::::When His Majesty is in Canada next month, there will be flags. They might not all be identical in proportion. Someone will be organising them, so you might want to ask the Governor General's office what shape they are. Hogweard (talk) 10:33, 4 May 2025 (UTC)

:::::::I recently noticed the news that King Charles III is about to visit Canada. I think it is better to wait and see the actual use. At first, I only found that the proportions of these two flags have changed, which is inconsistent with the previous flags. Moreover, when this flag was announced in 2023, it was not pointed out that its proportions have been modified compared with the flag used by the Queen in the past. 112.105.122.226 (talk) 13:48, 4 May 2025 (UTC)

:::::::So after more photos of the actual use of this flag appear, we will discuss how to modify the existing svg file. 112.105.122.226 (talk) 13:51, 4 May 2025 (UTC)

:::::::The ratios used for the flags are indeed not completely consistent, but I see that most of the flags use a ratio of 1:2. 61.216.108.176 (talk) 08:13, 28 May 2025 (UTC)

File:28_xiu.svg

;Article(s):

: Twenty-Eight Mansions

;Request:

: The Twenty-Eight Mansions Image is mirror reflected (specular reflection), which is wrong. If north is at the top, then east should be on the RIGHT. Or if east is on the left, then north should be at the BOTTOM. Can someone correct the image, please? -- UU (talk) 12:32, 1 May 2025 (UTC)

;Discussion:

:No knowledge of Chinese, but have used astronomical maps with similar mirroring. What if the original thing was meant to be hung up from the roof for the observer to see from below? Shyamal (talk) 10:09, 13 May 2025 (UTC)

:It's conventional to have east on the left etc for star charts e.g. :File:Field_Book_of_the_Stars-117-Constellations_of_Winter.svg. A better solution is to put a note in the caption to remind the reader. cmɢʟee⎆τaʟκ 17:28, 22 May 2025 (UTC)

Flag of Rathmines and Rathgar Urban District Council (1929–1930).svg

;Article(s):

: Rathmines and Rathgar, List of flags of Ireland, Saint Patrick's Saltire, Celtic cross

;Request:

: Could someone please create an SVG file of the flag used by the (now defunct) Rathmines and Rathgar Urban District Council from 1929 to 1930, as seen [https://www.crwflags.com/fotw/images/i/ie-rathmines.gif here]? Thanks. Snow Lion Fenian (talk) 15:31, 12 May 2025 (UTC)

;Discussion:

{{GLNF|Non-free image.ext|Diode bridge}}

Diodebridge-eng.gif

;Article(s):

: https://af.wikipedia.org/wiki/Diodebrug Diodebrug

;Request:

: I need a Afrikaans version with the following captions: Input must read Inset and DC Output must read GS Uitset. Regards Oesjaar (talk) 16:58, 14 May 2025 (UTC)

;Discussion:

Keep It Weird logo.webp|Keep It Weird logo

;Request:

: Hi! I am using the logo for a template on Commons but the white background is really distracting. Could anyone please remove it?--Trade (talk) 23:57, 14 May 2025 (UTC)

{{ping|Trade}} {{done}}--PBrieux (talk) 14:28, 29 May 2025 (UTC)

:@TradePlease update description with elements of the original one. Thanks. PBrieux (talk) 14:38, 29 May 2025 (UTC)

::@Trade if you don't use the image in an article, the image will be deleted. please read my talk page "Orphaned non-free image File:Logo for Keep It Weird.png" for instructions by bot on that matter. New png logo with transparent background will be deleted in 7 days. PBrieux (talk) 08:18, 2 June 2025 (UTC)

{{GLNF|CNNThisMorningAudieLog.png|PNG version of CNN This Morning with Audie Cornish logo}}

CNN This Morning with Audie Cornish logo.svg|Background-less SVG version (transferred to Wikimedia Commons if necessary)

;Article(s):

: CNN This Morning with Audie Cornish

;Request:

: Can anyone please vectorize PNG version of CNN This Morning with Audie Cornish logo with background removal. After that, if necessary, background-less version of the SVG file should be transferred to Wikimedia Commons. The PNG image can be seen in the article itself. -- 103.111.102.118 (talk) 04:24, 17 May 2025 (UTC)

;Discussion:

{{GLNF|RUTACA Airlines logo complete 2024-12-01.png}}

File:RUTACA Airlines logo (2025).svg

;Article

• RUTACA Airlines

;Request

Can someone please make a new svg format this logo. (google translator) AbchyZa22 (talk) 20:54, 18 May 2025 (UTC)

:Pinging @Minorax: AbchyZa22 (talk) 09:27, 30 May 2025 (UTC)

;Discussion

USAF Special Tactics Officer Emblem.jpg|U.S. Air Force Special Tactics Officer Emblem

;Article(s):

: United States Air Force special tactics officer

;Request:

: The U.S. Air Force Special Tactics Officer Emblem. An example of it can be seen on this [https://web.archive.org/web/20130711061145/http://www.afsoc.af.mil/specialtactics 2013 archived Air Force page]. Indefatigable2 ^talk 22:36, 18 May 2025 (UTC)

;Discussion:

;Article(s):

: Cyanometer

;Request:

: Please make downloadable, printable versions of the three cyanometer images shown in [https://bsky.app/profile/thisiscolossal.com/post/3loovhhyvds2n this Bluesky post] and at [https://www.thisiscolossal.com/2025/05/an-uncanny-postcard-fit-for-the-era-of-climate-catastrophe/].

Maybe they should be available as graphic files and PDFs? Andy Mabbett (Pigsonthewing); Talk to Andy; Andy's edits 14:53, 22 May 2025 (UTC)

;Discussion:

: {{i take}} Happy to make SVG and PDF versions if someone can ping me and provide the RGB colour value of each sector – measuring off a photograph will likely be inaccurate. cmɢʟee⎆τaʟκ 17:34, 22 May 2025 (UTC)

GLPK solution of a travelling salesman problem.svg|Illustration of travelling salesman problem

;Article(s):

: Travelling salesman problem and twenty-one other pages on fifteen projects

;Request:

: (1) The topmost dot of this illustration is cut off at the top. Can you extend the drawing and make the dot a full circle? (2) Once that's done, can you remove the lines and upload the result separately? In the travelling salesman problem article, it would be useful to have two images: first just the dots (an unsolved problem) and then the dots and lines (a solved problem). Nyttend (talk) 20:53, 23 May 2025 (UTC)

::{{Done}} I was able to create an unsolved version for you, yet since I lack the site permissions to replace another users images, I am personally unable to fulfill your first request. Hopefully someone else will. Sorry! Criticalistic (talk) 00:23, 24 May 2025 (UTC)

;Discussion:

{{float right clear none|{{switcher

|200px|Solved

|200px|Unsolved

}} }}

:{{done}} {{ping|Nyttend}} I've updated :File:GLPK_solution_of_a_travelling_salesman_problem.svg to match :File:Illustration_of_an_unsolved_travelling_salesman_problem.svg. Click the radio buttons or use arrow keys to confirm that the dots are aligned. cmɢʟee⎆τaʟκ 01:02, 24 May 2025 (UTC)

::cmglee, thanks! This image looks a lot better now. Criticalistic, thanks for the unsolved image! I've now added it to the article. For future reference — if you ever want to upload a new version of an image, but lack the user rights, you can always upload it separately and request that the files be merged. Most merger situations are caused by people not paying attention, but nobody will object if you say "I uploaded this separately because I couldn't overwrite the other one". Nyttend (talk) 21:20, 27 May 2025 (UTC)

:::Thanks for the tip Nyttend, will definitely be using that. Glad we could help. Criticalistic (talk) 02:11, 28 May 2025 (UTC)

;Article(s):

: Hypercomplex number, Subalgebra

;Request:

: Illustrations are particularly useful in algebra due to its abstract nature. The [https://ibb.co/MDXqhhMh illustration] was left at Talk:Hypercomplex number#Common associative algebras over the reals. It shows certain algebras and their supporting groups on basis elements. There are two lattices showing subalgebras and subgroups that correspond. It is requested that the illustration be put in a form appropriate for Commons as several articles might use it. The noted orders (a,b) in the group lattice can be omitted. — Rgdboer (talk) 22:00, 28 May 2025 (UTC)

┌──── Q ────┐
│     │     │
│    SBq    │
|     │     │
C ── Bc ── Bq
│     │     │
│    Sc     │
|     │     │
└─── Sq ────┘

;Discussion:

: {{ping|Rgdboer}} I don't know about this topic; is it ok to move the vertices around like this, to make the graph planar (edges don't cross) and rectilinear? cmɢʟee⎆τaʟκ 22:29, 30 May 2025 (UTC)

::No, the lattice indicates subalgebra by a descending line, vertical or slanted. Note for example that Complex is a subalgebra of Split-quaternion as indicated by a diagonal line. The top two algebras, Split-biquaternion and Biquaternion are independent, not connected. Similarly, the bottom two, Complex and Split-complex are not connected. Thus the display given is essential. — Rgdboer (talk) 20:22, 1 June 2025 (UTC)

File:common_associative_algebras_over_the_reals.svg

:::Just curious:

:::# Should the English text in the top figure and "Pauli group" be in italics?

:::# Should the "B" in Split-Biquaternion be in lowercase?

:::Cheers,
cmɢʟee⎆τaʟκ 16:52, 3 June 2025 (UTC)

::{{ping|cmglee}} This Commons image is excellent. As for the questions: Italics are not used for names of algebras and groups. Also, Split-biquaternion uses lower case b. Thank you for this very useful illustration of inclusions of algebras and their basis groups. The order notations (a,b) that are included correspond to data in List of small groups, but since the labels of groups are standard, the extra notation may confuse a novice. — Rgdboer (talk) 21:19, 3 June 2025 (UTC)

{{annotated image

|image=common_associative_algebras_over_the_reals.svg

|image-width=240

|height =85

|caption =Only the top half

}}

:::Thanks, {{ping|Rgdboer}} I've updated the italicisation and case.

:::I don't quite understand the following point. Do you mean to show only the top half? If so, one can use Template:CSS image crop or similar to display only the top half, as on the right. I've retained the bottom half in the image in case anyone wants to use it as an example.

:::Lastly, is it correct that Split-biquaternion is on the left column? Seems all the other splits are on the right. Was Split-biquaternion and Biquaternion accidentally swapped?

:::Cheers, cmɢʟee⎆τaʟκ 23:46, 3 June 2025 (UTC)

::{{ping|Cmglee}} Thank you for the updates. A first post has been placed at Galois connection where it is apparent that two lattices are in correspondence. The comment about confusing notation refers to the ordered pairs (a,b) in the group lattice. These numbers refer to the List of small groups but really are unnecessary for identifying the groups. Your note about split-biquaternion in the left column, while split-quaternion and split-complex are in the right, asks if a mistake has been made! No, the inclusions are correct. The terminology is explained at split algebras. The only non-split algebras in the lattice are quaternions and complex numbers. — Rgdboer (talk) 21:36, 4 June 2025 (UTC)

style="float:right;" | File:common_associative_algebras_over_the_reals.svg | File:common_associative_algebras_over_the_reals.svg

:::OK, I've removed the pairs from the default version. To get them back, use the old English version (lang=ang) as on the right. Thanks, too, for explaining. cmɢʟee⎆τaʟκ 12:47, 5 June 2025 (UTC)

{{-}}

Flag of Ohey.gif|Flag of Ohey (GIF version)

Flag of Ohey.svg|Flag of Ohey (SVG version)

Blason ville be Ohey.svg|Coat of arms of Ohey

;Article(s):

: Ohey

;Request:

: Hi! I was wondering if someone can kindly please vectorize the flag of Ohey? The flag consists of three yellow combs on a red background. When this is done, can that same person also overwrite the coat of arms of Ohey shown here with a design using the combs from the vectorized flag? The current version of the coat of arms is drawn badly and so needs replacement. Thanks in advance! -- 51.37.103.111 (talk) 19:53, 30 May 2025 (UTC)

;Discussion:

{{I take|koohikoo}}

:Hi, working on this, I'm noticing that the [https://www.ohey.be/ municipal website] for Ohey has the coat of arms as already uploaded, and looking at [https://www.google.com/maps/@50.4360304,5.1205222,3a,15y,106.59h,97.38t/data=!3m8!1e1!3m6!1s6CGiffVJebJrBKLetBdOeA!2e0!5s20210901T000000!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fcb_client%3Dmaps_sv.tactile%26w%3D900%26h%3D600%26 streetview], the Administration communale has the wallonian flag, but not the flag you've linked. Are you sure this is a change that needs to be made? — Preceding unsigned comment added by Koohikoo (talk • contribs) 23:44, 31 May 2025 (UTC)

::I have sone the shield in any case. The flag could be taken from that. Hogweard (talk) 14:54, 5 June 2025 (UTC)

:::{{Done}} Hogweard (talk) 22:03, 5 June 2025 (UTC)

{{GLNF|File:Autonomy Corporation logo.svg|Autonomy Corporation logo}}

;Article(s):

: HP Autonomy

;Request:

: Contains hundreds of layers to draw the circle. Excessively large (>1 MB) for this logo. --Min☠︎rax^«¦talk¦» 08:41, 1 June 2025 (UTC)

;Discussion:

;Article(s):Hyperbolic coordinates#Trigonometry

;Request:

: The article-section Hyperbolic coordinates#Trigonometry refers to a rhombus with diagonal along y = x as follows:

:"The hyperbolic functions sinh, cosh, and tanh can be illustrated with hyperbolic coordinates. Let

:$A\; =\; (e^t,\; e^\{-t\}),\; \backslash \; B=(e^\{-t\},\; e^t),\; \backslash \; C\; =\; (e^t\; +\; e^\{-t\},\; e^t\; +\; e^\{-t\})\; .$

:Then BCAO forms a rhombus with diagonals intersecting at $M\; =\; (\backslash frac\{e^t\; +\; e^\{-t\}\; \}\{2\},\backslash \; \backslash frac\{e^t\; +\; e^\{-t\}\; \}\{2\}\; )$. The hyperbolic cosine is defined as $\backslash cosh\; t\; =\; \backslash frac\{e^t\; +\; e^\{-t\}\; \}\{2\},$ so M = ( cosh t, cosh t)."

The image currently used in that article shows a half-rhombus with segments corresponding to sinh and cosh. An illustration of the suggested rhombus is requested. The vertices (A, B, C) and the semi-diagonals intersecting at M are the only details needed, and they are given in the above text. — Rgdboer (talk) 22:02, 4 June 2025 (UTC)

;Discussion:

: The "coordinates" of C has a single value, not a pair. Is $e^t\; +\; e^\{-t\}$ both the x and y value? cmɢʟee⎆τaʟκ 15:36, 5 June 2025 (UTC)

::Yes, you caught a mistake, and the correction is as you say. Correction in place now at Hyperbolic coordinates. That detail was a blemish. — Rgdboer (talk) 21:51, 5 June 2025 (UTC)

:::File:cartesian_hyperbolic_rhombus.svg⎆τaʟκ 23:00, 5 June 2025 (UTC)]]

::{{ping|cmglee}} Thank you for an excellent illustration. It has been placed in § Trigonometry of Hyperbolic coordinates. — Rgdboer (talk) 21:58, 6 June 2025 (UTC)

:::Thanks, @Rgdboer. I noticed that you changed t in the equations to u. If I understood correctly, ±t is the exponent at points A and B whereas u in the diagram is the angle MOA. As u also represents a coordinate in the first diagram in the article, should we retain t in the equations but change u in the diagram to, say, θ? cmɢʟee⎆τaʟκ 22:23, 6 June 2025 (UTC)

::The change from t to u makes an agreement between the diagram and the text. Indeed, u is the angular parameter for the hyperbolic functions and it is also the parameter of the exponential function. The point is that commonly sinh and cosh are defined using the exponential function without reference to hyperbolic coordinates, and the diagram now shows how that common usage refers to geometry. — Rgdboer (talk) 22:45, 6 June 2025 (UTC)

:::Thanks for explaining. I learnt something today. cmɢʟee⎆τaʟκ 07:07, 7 June 2025 (UTC)

Seal of the United States Small Business Administration.svg|The seal on the actual flag seems to have some differences

;Article(s):

: Small Business Administration

;Request:

: Based on [https://www.facebook.com/share/19QmBCPR2K/]. The seal is now having a red border, while the U.S mainland's shape also loses the outer red border line. --  Hwi.padam   03:48, 5 June 2025 (UTC)

;Discussion:

;Article(s):

: Alice Heine

;Request:

: I believe Alice Heine should have a coat of arms, all other Monégasque consorts have them uploaded. -- EmilySarah99 (talk) 10:33, 6 June 2025 (UTC)

;Discussion:

File:Log-pole-x_1.svg

File:Hyperbolic_sector.svg

;Article(s):

: Hyperbolic sector#Hyperbolic logarithm

;Request:

:In the article-section Hyperbolic sector#Hyperbolic logarithm one finds the following text:

"To accommodate the case of negative logarithms and the corresponding negative hyperbolic angles, different hyperbolic sectors are constructed according to whether x is greater or less than one. A variable right triangle with area 1/2 is $V\; =\; \backslash \{(x,\; 1/x),\; \backslash \; (x,0),\; \backslash \; (0,0)\backslash \}\; .$ The isosceles case is $T\; =\; \backslash \{(1,1),\backslash \; (1,0),\backslash \; (0,0)\backslash \}.$ The natural logarithm is known as the area under y = 1/x between one and x. A positive hyperbolic angle is given by the area of

$\backslash int\_1^x\; \backslash frac\{dt\}\{t\}\; +\; T\; -\; V.$ A negative hyperbolic angle is given by the negative of the area $\backslash int\_x^1\; \backslash frac\{dt\}\{t\}\; +\; V\; -\; T.$ This convention is in accord with a negative natural logarithm for x in (0,1)."

The object is to show that hyperbolic sector area to y = 1/x is the same as the log area. There are two cases: x in (0,1) and x > 1. The method uses addition and subtraction of right triangles. Illustrations are requested to show the equality of areas. — Rgdboer (talk) 22:35, 6 June 2025 (UTC)

;Discussion:

File:Visual_proof_hyperbolic_segment_subtended_area.svg

:I can't think of a way to show that the areas are equal. Only after drawing this, I realised that I could prove it only if S is the midpoint of OR. In the above diagram, if S is at 1, R must be at 2, unless b can be shown to equal d.

:Can you sketch, perhaps on paper, how you could explain it? Cheers, cmɢʟee⎆τaʟκ 22:43, 7 June 2025 (UTC)

::Ok, your diagram does combine the two given. Some of your variables are supposed constant: S = (1,0) so that P = (1,1). Then 0PS is triangle T given in the text. Next R = (x. 0) so Q = (x, 1/x) so triangle 0QR is the variable triangle called V in the text. Both of these triangle have area 0.5 . The argument is similar to a tangram puzzle where blocks are moved around. Here one triangle is added to a figure, then the other triangle removed. Since they both have area ½ the area after the addition and subtraction is the same as area before. Try considering only x > 1 first (as in your illustration) since complications arise due to signed areas in the general case. — Rgdboer (talk) 21:57, 8 June 2025 (UTC)

Burgee of the Humber Yawl Club.svg

;Article(s):

: Humber Yawl Club, Flags and symbols of Yorkshire, List of United Kingdom flags

;Request:

: Could someone please create an SVG file of the burgee used by the Humber Yawl Club, as seen [https://upload.wikimedia.org/wikipedia/commons/4/47/Hycgraphic.gif here]? Thanks. Snow Lion Fenian (talk) 13:35, 8 June 2025 (UTC)

;Discussion:

Flag of the Cornish Maritime Trust.svg

;Article(s):

: List of Cornish flags

;Request:

: Can somebody please create an SVG file of the pennant used by the Cornish Maritime Trust, shown [https://i2-prod.cornwalllive.com/incoming/article9236411.ece/ALTERNATES/s1227b/0_GMP_DCM_190424Barnabas_012JPG.jpg here], [https://i2-prod.cornwalllive.com/incoming/article9236406.ece/ALTERNATES/s1227b/0_GMP_DCM_190424Barnabas_010JPG.jpg here] and [https://www.falmouthpacket.co.uk/resources/images/18028780/?type=responsive-gallery-fullscreen here]? Thanks. Snow Lion Fenian (talk) 13:52, 8 June 2025 (UTC)

;Discussion: