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1392:: two triangles can't be in axial perspective unless there exists a plane containing both. So if we replace "projective spaces" by "projective planes" throughout the article then there are fewer cases to explain in this lead paragraph. But that would be a significant rewrite, and I'm not sure whether it's justified by the sources.
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There is a nice practical application in perspective drawing: suppose you have two (or more) lines drawn in perspective, which meet at a vanishing point located far enough away from the physical page to be constructed directly. Desargues' theorem can be used to construct additional lines which meet
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So these geometric transforms can be easily be written in elementary matrices coordinate system independently, i.e., we don't have to project objects only to those coordinate planes in order to simplify the projection matrix establishment procedure: the projection matrix which projects objects to an
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article hadn't yet been created. I would prefer not to merge, as I think that perspective triangles are important enough, that there are enough results about them that are distinct from
Desargues' theorem, and that there are enough other topics already included in the Desargues theorem article that
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Proper nouns that end with s: There is tension in
English over whether just an apostrophe, or an apostrophe and the letter s, should be added to such proper nouns (James' house or James's house, but be consistent within an article). Some forms always take an extra s (Ross's father); some, mainly
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The
Concise Oxford Dictionary of Mathematics, and Britannica (at least as far back as 1986, the publication year of my hard copy) write it as "Desargues's theorem," as do the more authoritative sources on the web, although a majority of pop writers still seem to be using the old style. Journal
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It doesn't matter whether the projective plane is self-dual; what matters is that the statement is self-dual. That is, the dual of the statement is the same statement. So if you prove the statement in some plane (self-dual or not) you have also proved the dual of the statement.
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It is possible for ten points and ten lines in the plane to be so arranged that each of the ten lines passes through three of the ten points and each of the ten points lies on three of the ten lines, even though that whole configuration is
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I edited the POTD caption to avoid using the word "produced". I agree that it is exactly the right technical term for the line that contains a line segment, but we should avoid jargon that is likely to be unfamiliar to non-geometers.
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Although omitting the s used to be the norm for such names (I was raised in the pro-omission tradition and have been accustomed until recently to writing it as
Desargues'), more recent sources such as the 1961 edition of Coxeter's
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A better question might be: Specifically what other relations of
Desargues' theorem to concepts in mathematics do you have in mind other than perspective triangles? The theorem should be merged into the definition if anything.
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Compass and Ruler is written in Java by von R Grothmann. This program is excellent. It is very well written, in Java and available for Mac or
Windows or Linux, and it is free with source code too. Its home page is at
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Maybe you thought of a solution but didn't actually implement it. The caption still said "produced" when I looked at it. I've made a change, but feel free to edit this further if you can think of a better way.
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The CC license for this image does call for attribution when it is used (remixed in your case). Try
Googling Desargues theorem images, I'm sure that you'll find one that doesn't ask for attribution.
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axially perspective which makes the proof in 3 dimensions so easy. I've done what I can for this article - if only I had an additional 24 hours or had this occurred in a different week - Oh well!
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Does anyone have any strong opinions either way? In particular are there any strong objections to matching
Knowledge's style in the case of Desargues to the usage of the sources cited above? --
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I'd like to use the image on the t-shirts we give away to students in out local high school mathematics contest. I don't really want to write an attribution on the shirt. Would that be okay?
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1087:§ Detailed proof via homogeneous coordinates representation of the extended Desargues theorem, and its applications in computer graphics can be seen from the link below:
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editors these days seem to be encouraging its inclusion (I was recently picked on by one for using the old style and adapted accordingly).
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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I also have trouble with the proof. It depends on various lines being "concurrent," but "concurrent is nowhere defined.
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I agree that the lead could use a rewrite, but I can't do it in the amount of time left. The suggestion about replacing
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The article hand-waves it away by saying it follows by duality. But some projective planes are not self-dual. --
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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doesn't work, since it is precisely that two triangles in different planes which are centrally perspective are
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Specifically, what results about perspective triangles other than
Desargues' theorem do you have in mind?
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I don't understand from the proof... I can't see the equivalence with those scalar & cross products.
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Great god.... even esoteric subject get a fine treatment. Thanks to whoever contributed to this article.
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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Sorry, I meant that I changed it in the POTD box. I didn't make the same change to the actual article. —
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arbitrary plane is actually an elementary matrix in very simple form which we can easily write it out!
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Biblical and
Classical, usually do not (Socrates' wife; Moses' ascent of Sinai; Jesus' last words).
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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The 3-dimesional proof depends on various lines being "concurrent." Please define "concurrent."
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is somewhat clumsy. I'm used to thinking about Desargues's theorem as a result about projective
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before doing mass systematic removals. This message is updated dynamically through the template
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https://web.archive.org/web/20090321024112/http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm
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Not a matter for concern on a par with the current state of the economy, but Knowledge's
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If you found an error with any archives or the URLs themselves, you can fix them with
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they are in perspective centrally. Lines through the triangle sides meet in pairs at
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incidence-isomorphic to the Desargues configuration. Should that be mentioned here?
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Since this hasn't any opposition for quite a while, I'll just remove the template.
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Please add the date when this theorem was discovered or proved or conjectured --
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that we can use and build example files to go along with article and theorems.
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I have two concerns, although I'm not sure of the best way to address them.
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has a license that doesn't require attribution, and might fit your needs. —
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it would be confusing to link to it under the perspective triangle name. —
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http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/java/zirkel/index.html
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are tetrahedrons or at most one of them is quadrangle. In this case, the
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along the axis of perspectivity. Lines through corresponding pairs of
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on the triangles meet at a point called the center of perspectivity.
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Extended Desargues' theorem and Its Application in Computer Graphics
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Hello! This is a note to let the editors of this article know that
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on November 2, 2011. You can view and edit the POTD blurb at
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for additional information. I made the following changes:
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You might also try looking at some of the other images in
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and was forced to resort to MathWorld instead, as the
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Added. As always, feel free to reword my addition. —
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http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm
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1688:This message was posted before February 2018.
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38:It is of interest to the following
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212:application in perspective drawing
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1811:Mid-priority mathematics articles
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793:{\displaystyle ABCD-S-A'B'C'D'}
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1147:{\displaystyle Stereohomology}
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109:and see a list of open tasks.
1806:C-Class mathematics articles
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1761:Proof of converse statement?
1568:File:DesarguesHessenberg.svg
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481:{\displaystyle ABC-S-A'B'C'}
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368:Non-Desargues configuration
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1655:Hello fellow Wikipedians,
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1194:{\displaystyle elementary}
325:Desargues' or Desargues's?
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1665:
1661:
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1650:
1648:
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1531:
1521:
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1511:
1507:
1503:
1502:
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1458:
1454:
1449:
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1447:
1446:
1442:
1438:
1430:
1426:
1422:
1418:
1417:automatically
1414:
1410:
1406:
1405:
1404:
1403:
1399:
1395:
1391:
1387:
1382:
1380:
1379:when produced
1375:
1369:
1365:
1360:
1354:
1350:
1346:
1342:
1338:
1334:
1333:
1328:
1321:
1315:
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1303:
1298:
1297:
1289:
1285:
1281:
1277:
1269:
1266:
1264:
1263:
1256:
1243:
1240:
1236:
1222:
1219:
1216:
1213:
1210:
1207:
1188:
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1182:
1179:
1176:
1173:
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1167:
1164:
1161:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1114:
1111:
1108:
1105:
1102:
1093:
1092:
1088:
1085:
1070:
1067:
1062:
1059:
1038:
1035:
1015:
1012:
1009:
988:
985:
980:
977:
956:
953:
933:
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917:
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890:
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864:
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848:
845:
840:
837:
816:
813:
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786:
783:
778:
775:
770:
767:
762:
759:
755:
752:
749:
746:
743:
740:
737:
728:
713:
710:
706:
685:
682:
678:
657:
654:
650:
630:
609:
606:
585:
564:
561:
540:
519:
516:
495:
474:
471:
466:
463:
458:
455:
451:
448:
445:
442:
439:
436:
420:
416:
412:
408:
407:
406:
405:
401:
397:
396:Michael Hardy
391:
390:
386:
380:
379:
378:
376:
367:
365:
364:
360:
356:
355:Vaughan Pratt
351:
348:
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336:
335:
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332:
320:
313:
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308:
299:
292:
287:
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285:
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283:
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273:
269:
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264:Michael Hardy
261:
260:
259:
258:
257:
256:
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224:
223:
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219:69.174.67.197
211:
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187:
183:
181:
176:
175:
169:
163:
161:
160:
142:
138:
132:
129:
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125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
1764:
1742:
1739:
1714:source check
1693:
1687:
1684:
1657:
1654:
1633:
1626:
1608:— Preceding
1605:
1586:
1534:142.27.68.70
1528:— Preceding
1525:
1486:
1433:
1416:
1412:
1408:
1389:
1385:
1383:
1378:
1376:
1373:
1330:
1292:
1273:
1251:<ref: -->
1247:Cite error:
1244:
1241:
1237:
1094:
1089:
1086:
729:
428:
394:
374:
371:
352:
346:
343:
337:
328:
233:
215:
192:— Preceding
189:
184:
177:
170:
167:
156:
137:Mid-priority
136:
96:
62:Mid‑priority
40:WikiProjects
1341:perspective
331:style guide
112:Mathematics
103:mathematics
59:Mathematics
1800:Categories
1751:Report bug
1249:There are
1734:this tool
1727:this tool
1359:DynaBlast
1337:triangles
1288:Main Page
1255:help page
1740:Cheers.—
1610:unsigned
1530:unsigned
1453:Jowa fan
1394:Jowa fan
1353:vertices
1343:axially
1295:howcheng
488:, where
236:recently
194:unsigned
1767:Svennik
1664:my edit
1589:Aliotra
1364:Archive
1357:Image:
1339:are in
180:Xah Lee
159:Xah Lee
139:on the
30:C-class
1413:planes
1409:spaces
1390:planes
333:says:
36:scale.
1504:Done
1787:talk
1771:talk
1642:talk
1634:Done
1618:talk
1593:talk
1576:talk
1554:talk
1538:talk
1510:talk
1493:talk
1471:talk
1457:talk
1441:talk
1425:talk
1398:talk
1302:chat
1051:and
969:and
829:and
699:and
598:and
553:and
508:and
415:talk
400:talk
359:talk
268:talk
249:talk
202:talk
1708:RfC
1678:to
1411:by
1325:In
375:not
131:Mid
1802::
1789:)
1773:)
1721:.
1716:}}
1712:{{
1644:)
1620:)
1595:)
1578:)
1556:)
1540:)
1512:)
1495:)
1473:)
1459:)
1443:)
1427:)
1400:)
1366:–
1329:,
1257:).
1028:,
1002:,
800:.
756:−
750:−
727:.
671:,
578:,
533:,
452:−
446:−
417:)
402:)
361:)
270:)
251:)
204:)
1785:(
1781:—
1769:(
1753:)
1749:(
1736:.
1729:.
1640:(
1616:(
1591:(
1574:(
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1435:—
1423:(
1396:(
1304:}
1300:{
1223:x
1220:i
1217:r
1214:t
1211:a
1208:m
1189:y
1186:r
1183:a
1180:t
1177:n
1174:e
1171:m
1168:e
1165:l
1162:e
1142:y
1139:g
1136:o
1133:l
1130:o
1127:m
1124:o
1121:h
1118:o
1115:e
1112:r
1109:e
1106:t
1103:S
1071:′
1068:D
1063:′
1060:A
1039:D
1036:A
1016:.
1013:.
1010:.
989:′
986:B
981:′
978:A
957:B
954:A
934:6
931:=
926:2
921:1
918:+
915:3
911:C
907:=
902:2
897:1
894:+
891:n
887:C
865:′
862:D
857:′
854:C
849:′
846:B
841:′
838:A
817:D
814:C
811:B
808:A
787:′
784:D
779:′
776:C
771:′
768:B
763:′
760:A
753:S
747:D
744:C
741:B
738:A
714:′
711:C
707:C
686:′
683:B
679:B
658:′
655:A
651:A
631:S
610:′
607:C
586:C
565:′
562:B
541:B
520:′
517:A
496:A
475:′
472:C
467:′
464:B
459:′
456:A
449:S
443:C
440:B
437:A
413:(
398:(
357:(
266:(
247:(
200:(
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
