Talk:Malfatti circles

Triangular prism or rectangular wedge
I believe these two terms are equivalent, so it's essentially a matter of taste. I think I'd leave it "rectangular wedge" simply b/c the original author called it a "wedge". Justin W Smith talk/stalk 17:59, 7 July 2011 (UTC)
 * I suspect that the two 3-sided faces of a triangular prism need not be orthogonal translations of each other, further strengthening the argument for calling it a "rectangular wedge". Justin W Smith talk/stalk 18:02, 7 July 2011 (UTC)
 * Wedge (geometry) says that "A triangular prism is a special case wedge with the two triangle faces being translationally congruent.". Ignoring the poor grammar, this suggests that triangular prism is the more specific term. Of course, the case we need here is even more specific, an orthogonal translation. —David Eppstein (talk) 18:28, 7 July 2011 (UTC)
 * I don't think it needs to be a right prism; isn't the problem essentially the same if the whole figure is sheared? On second thought, that would make the cylinders elliptical. —Tamfang (talk) 02:53, 13 July 2011 (UTC)
 * On third thought, if the 'side' planes of a right prism are held constant and the 'base' planes moved but kept parallel and the distance between their intercepts kept constant, circular cylinders can be drawn within the sheared prism with the same volume as before. —Tamfang (talk) 04:42, 6 August 2011 (UTC)


 * What is a rectangular wedge? If it's a wedge whose three quadrilateral faces are rectangles, that's a right prism.  If it's a wedge with only one rectangular face, I don't believe that can be what Malfatti had in mind; the optimum (granting Malfatti's mistaken assumption) would depend on the angle between the end-planes. —Tamfang (talk) 02:53, 13 July 2011 (UTC)

How on earth...
..can someone believe these circles will have the maximum surface? If you think about it for half a minute you realise that in a very sharp-angled triangle this would obviously be wrong. It's hard to understand that a mathematician could come to such a conclusion... Bizarrrr.. 84.197.187.25 (talk) 13:16, 9 February 2012 (UTC)

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Labeling at Steiner's pic
@Chiswick Chap, thank you for taking care! I did not know about the labeling at all, until I, just by chance, clicked within the pic. Then I supposed it would be some secret thumbnail feature, and therefore added to the caption. I still do not see the labeling in my standard scaling setting (110%), but found out that rendering the screen at >100% (1920x1080, Win 10, Firefox) makes the labeling disappear. Scalings below 100% work fine. I have no idea what makes the fineprint (dashed lines) render OK, and hides the labels. (to be honest, the labels are somewhat big now) Purgy (talk) 14:26, 21 March 2018 (UTC)
 * I can't reproduce your problem despite trying many scalings. I'll make the labels a little smaller. Chiswick Chap (talk) 14:59, 21 March 2018 (UTC)
 * I think it's probably a browser caching issue. I was seeing unlabeled and non-circular images until I refreshed. —David Eppstein (talk) 16:15, 21 March 2018 (UTC)
 * Being now explicitly aware of the existence of different versions of the pic, and since the labels are visible now also in my standard scaling, I am strongly inclined to cling to the caching issue. Thank you cordially, both. Purgy (talk) 09:25, 22 March 2018 (UTC)

Remarks about Zalgaller and Los
Dear Prof. Eppstein,

Given that you do not reply at your email and at your talk page, please find a copy of my remarks here.

You did not unfortunately reply to my email, sent at your academic address. Therefore, I found back my Wikipedia account and I post the essentials here, where I was suggested to reply to your repeated amendments to the page.

I am the author of the following paper:

Lombardi, Giancarlo (June 2022), "Proving the solution of Malfatti's marble problem", Rendiconti del Circolo Matematico di Palermo, Series 2, doi:10.1007/s12215-022-00759-2.

I was surprised to find the following statements about my work, conducted privately at my living place (this is why there is no affiliation):

"Undo continued promotionalism, apparently by someone trying to hype up their own research. Z&L 1994 claim to have a proof of a solution. Andreatti et al accept it as a proof. It uses some computer-based calculations but that does not make it less of a proof. Another proof that avoids the calculations is a good thing, but not something to be trumpeting from the rooftops."

You state further that "Previous proof appears to have been fully rigorous": if it was, I would have not carried out my work in its form and I would have titled the paper instead: "A new simpler proof of the solution of Malfatti's marble problem". My work was peer reviewed during two years.

By a deeper analysis, the work of Zalgaller and Los is not a proof in mathematical sense. In the introduction I used a language customary in science work and I did not list in detail the sequel of encountered substantial flaws. Just to mention the most crucial ones, several functions, essential in the proof, are stated to be increasing or decreasing without proof and referring only to a numerical table. This is in particular the case of alpha0 and gamma0, the latter fundamental in the proof. It is stated that alpha0-alpha2(t) has a single zero in the concerned t interval and this is not shown either. Above all, the entire final part of the reasoning is constituted by a numerical verification of an inequality (looking like the "proof" of Goldberg 1967).

You do not contradict that by stating that "It uses some computer-based calculations", but you conclude "that does not make it less of a proof".

In that respect I refer to the Kepler Conjecture and in particular to the first Hales' Proof. Hales uses numerical computation to find lower bounds: it is what I do with the final lower bound value on Gamma in the marble problem. In that case a numerical computation has the value of a proof, because it has in its own purpose a finite numerical precision, as sufficient to find a lower bound. On the contrary, the statement that a function is increasing or decreasing by plotting or, further, that a function admits a single zero in an interval, again by plotting, does not provide any proof, as it would require infinite numerical precision, which is impossible. The numerical justification of an inequality may enjoy a similar problem. I am an engineer and in practical projects one accepts this kind of statements, as providing a functioning circuit or system as a result. But I would never use such a statement as a "proof" of a given property, but only as an indication that this happens in the practice. Moreover, Hales himself was not fully convinced by the numerical nature of the proof and he found necessary to give a "formal proof".

In the peer reviewed introduction I state synthetically all those facts and the conclusion is that I provide an analytical proof, whereas previously there was a justification based on conjectures stated from numerical simulation. And this proof is the first one since the problem was posed in 1803. Therefore, whoever wrote made no promotionalism nor trumpets, but indicated mere facts and the reviewers agreed with them by accepting title, abstract, introduction and conclusions.

I thank you for your kind attention and I ask you please not to curb facts and to revert finally the text providing the real situation. In math there are facts and not opinions.Gialom05 (talk) 04:37, 24 June 2022 (UTC)