Charles Link's latest activity
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Charles Link reacted to anuttarasammyak's post in the thread Undergrad Finding the minimum distance between two curves with
Like.
Find the two points that share the same normal line. It would be a general way as @pasmith showed. -
Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.Excellent. By @Gavran's method, I have ## x_2=\frac{a}{5}+\frac{12}{5} \approx 2.54 ##. :) (see also posts 24, 25, 29, and 30). Note...
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Charles Link reacted to anuttarasammyak's post in the thread Undergrad Finding the minimum distance between two curves with
Agree.
I got ##x_1=1.8317... \ x_2=3-\frac{x_1}{4}=2.5421...## The equation of ##x_1##: Other two casese : ##(x_1.x_2)=(-1.3444... -
Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.Please see the edits to my post 25. Thanks. <3 and I let Wolfram solve it: Three real roots. The smallest one is the one of interest...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@DaveE These two are no longer identical parabolas, but I believe @Gavran 's method will work for them. I'll try to post the result...
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Charles Link reacted to DaveE's post in the thread Undergrad Finding the minimum distance between two curves with Like.
Excellent! Symmetry again. What about the curves y=4-x^2 and y=(2x-3)^2? Or y^2=x and y=(x+10)^2? I've given this zero thought, but I...
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Charles Link replied to the thread Undergrad Finding the minimum distance between two curves.@Gavran has an interesting way to solve problems of this type when the curves are to the second power. I thought I'd try his method on...
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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.
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Charles Link reacted to mfb's post in the thread Artemis 2 launch - humans return to the Moon after 54 years with Like.
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...
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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.