Talk:Squaring the circle/Archive 1

message: If I remember correctly, there was an article in New Scientist several years ago about a mathematician who squared the circle by dividing it into a finite number of fractal-edged pieces. I have looked on Google, but I can't seem to find any more info about this. Has anyone heard of it? Axl 21:48, 14 Dec 2004 (UTC)
replies: text: The mathematician was Laczkovich. See Tarski's circle-squaring problem. There really should have been a link to this article, so I'll add one now. --Zundark 22:05, 14 Dec 2004 (UTC)

text: Thanks, Zundark. :-) Axl 17:02, 15 Dec 2004 (UTC)
thread_title:  Fractals? 

message: : According to Drini's earlier comments to Zoe, substantive edits constitute reverts. That's aside from his notation of them, and the fact that there is supposed to be discussion first not after a change and that the attitudes evidenced are rather unwiki. It's neither lying nor inappropriate to remind someone that they are pushing a limit.Rktect 10:33, 13 September 2005 (UTC)
replies: text:  I've pointed my changes below, and the claim was that if consecutive edits reconstruct a previous version in the same way a revert would, then yes, it is considered. But I checked the previous version and the first 3 edits were not a revert, only the 4th, but even if you stretch that in your mind, it would account to 2 reverts, not breaking 3RR as you falsely accused me.  -- (☺drini♫|☎) 15:50, 13 September 2005 (UTC)
thread_title: drini

message: Much of the information contained in the article is incorrect.  A square with an area identical to the area of a given circle cannot exist in the real world.  It is irrelevant what instrument is used to construct the square. The problem does not "become trivial".  The impossiblity results from the fact that pi is a transcendental number.  No real world object with length which is a multiple of pi can exist, even though the length can approximate a multiple of pi as closely as we would like.  To construct a square with the same area as a given circle would require that the length of the sides of the square be a multiple of pi. 128.238.44.102 16:50, 12 September 2005 (UTC)
replies: text: The comment above is a misunderstanding.  The problem of squaring the circle is not about physical objects with circular shapges; it's about an abstract mathematical object: Euclidean space.  And your assertion that physical objects cannot have ratios of lengths that are transcendental numbers I find very dubious. Michael Hardy 23:17, 12 September 2005 (UTC)
thread_title:  revision needed 

message: Sorry to start a new section, but I am a bit confused. Can I deduct from the above that the opinion of rktect is that the ancient Egyptians were familiar with Bresenhams algorithm, and that the Egyptians (or their architects) used it to solve the squaring of the circle problem in an analytical manner? Just curious. -- Egil 13:33, 24 September 2005 (UTC)
replies: text: Ancient math often does have implications for modern problems. The ancient Egyptians were familiar with the use of inscription grids which allowed them to draw a slope at a unit rise and run and in a similar manner to describe a circle. Modern mathematicians also find such graphs useful. You can read the rest of the comments to find out about the Egyptians method for finding the area of a circle that was a good aproximation to the area of a square. Rather than saying that the Egyptians were familiar with Bresenham's circle algorithm, or that he was familiar with the Rhind papyrus (which is more likely), its probably best to allow that both worked independant solutions to a similar problem. What Bresenham's algorithm leads to is first polylines and then nurbs and splines. I'm sure drini is familiar with them and can explain to you how the math works. Rktect 01:08, 25 September 2005 (UTC)
replies: text: I take it that What Bresenham's algorithm leads to is first polylines and then nurbs and splines. is a theory of yours based on the same sort of insight in computer graphics algorithms that you have in subjects like ancient Egypt? -- Egil 07:58, 25 September 2005 (UTC)
replies: text:  You should credit Donald Hearn/M. Pauline Baker. Although in both cases the knowledge is based on solid research its not my original research. Donald Hearn/M. Pauline Baker "Computer Graphics" Prentice Hall, 1986  Chapter 3 Output Primatives p 76 Exercise 3.2 "Extend Bresenham's line algorithm to generate lines with any slope. Implement the polyline command using this algorithim as a routine that displays the set of straight lines between the n output points. For n = 1 the routine displays a single point." Rktect 17:16, 25 September 2005 (UTC)
replies: text: The "source" you are citing is simply a textbook in computer graphics, where the student is asked to expand an implementation of Bresenhams line drawing algorithm so that it can handle polylines. In fact, I'm afraid your statement "What Bresenham's algorithm leads to is first polylines and then nurbs and splines." is just as meaningless as saying that "What the espresso machine leads to is coffee plants.". But thanks for the insight. -- Egil 06:29, 27 September 2005 (UTC)
thread_title:  More on Bresenham 

message: The section Modern approximations has a hall of fame: Ramanujan, one C. D. Olds, Martin Gardner, and one B. Bold [is that WP:BOLD?], who allegedly all gave geometric constructions for 355/113. Is that worth remarking? Who are these Olds and Bolds, and why is it remarkable that anyone (including no-one less than Ramanujan) gave such a construction unless there is something notable about the construction specifically -- in which case we should read here what that is. Any ancient Greek geometer could have constructed 355/113, they only did not know it was a good numerical approximation. I can construct 21053343141/6701487259 = 3.14159265358979323846238... . If I manage to get that published in the Journal of Incredibly Tedious Mathematics, will I be induced in the Wikipedia Hall of Fame? LambiamTalk 10:59, 17 April 2006 (UTC)
replies: text: I have seen some of these constructions; they are fairly elegant, but would be tedious to describe without a diagram (most of them depend on 113 = 7² + 8²). I would leave this in, and possibly ask someone with the tools to make a diagram or two. Septentrionalis 14:27, 17 April 2006 (UTC)
replies: text:  I have tried to expand the introduction to the section to make it clearer what it is about. But the relevance entries are really impossible to judge without having some measure of how complex each of the constructions is. Could someone in the know please provide an indication of this? Henning Makholm 09:46, 28 May 2006 (UTC)
thread_title:  Approximations using rationals