Charles Link's latest activity
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If you want visit @fresh_42 he has been at our political community https://civicswatch.com/. He may still return here when ready. -
Charles Link reacted to mfb's post in the thread Artemis 2 launch - humans return to the Moon after 54 years with
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The Artemis program in the US aims to return to the Moon, land, and work on long-term expeditions and a permanent Moon base. At least... -
Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.I would like to give a big thank you to @anuttarasammyak , @pasmith , @Gavran , and @DaveE for their inputs to this thread. I really...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@Gavran Very good. I think your Vieta calculation above might have come from Wolfram. My apologies if I am incorrect. When I...
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Charles Link reacted to Gavran's post in the thread Undergrad Finding the minimum distance between two curves with Like.
Analytical solution by using Vieta's substitution: ## \begin{align} &a^3-9a^2+21a-3=0\nonumber\\...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@DaveE Excellent. In hindsight, your solution where you pointed out the inverted and translated symmetry of the two essentially...
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Charles Link reacted to DaveE's post in the thread Undergrad Finding the minimum distance between two curves with Like.
My approach relied on symmetry and geometrical reasoning with just a tiny bit of calculus. Since these two curves are translated and...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.Please see the two Edits added to post 16 above. I think they may be useful.
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@Gavran Very good=Excellent. :) You have an interesting approach where you translated the first curve by ## (a,b) ## until it made...
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Charles Link reacted to Gavran's post in the thread Undergrad Finding the minimum distance between two curves with Like.
Let ## (x_1,y_1) ## be a point on the curve ## f(x)=4-x^2 ##, which is the closest point on the curve ## f(x) ## to the curve ##...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.Just a couple additional comments: I thought I did pretty well by getting a numerical solution by writing out the partial derivative...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@pasmith I think it should read ##-2(x_1+x_2-3)=0 ##. Otherwise, yes, very good=excellent. :) and I think I see where he got the...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.Yes, sometime I'm going to need to try Vieta's substitution on this cubic and see if I can get the same answers that Wolfram got. :)...
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Charles Link reacted to pasmith's post in the thread Undergrad Finding the minimum distance between two curves with Like.
If $$L = (y_1(x_1) - y_2(x_2))^2 + (x_1 - x_2)^2$$ then the partial derivatives are $$\begin{split} \frac{\partial L}{\partial x_1} &=...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.For the calculation with the slopes mentioned in post 8, we have ## m=\frac{2-(4-a^2)}{3/2-a}=\frac{(3-a-3)^2-2}{3-a-3/2}## and these...