Charles Link's latest activity
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Charles Link reacted to kuruman's post in the thread Undergrad Trigonometry problem of interest with
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Here is the derivation mentioned in post #30. Refer to the figure on the right. It shows half the hexagon as a quadrilateral inscribed... -
Charles Link replied to the thread Undergrad Trigonometry problem of interest.@kuruman You essentially have the same solution for ## x=R ## in post 30 that @renormalize has, but you should recognize that the...
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Charles Link replied to the thread Undergrad Trigonometry problem of interest.@renormalize Thank you very much. :) You did verify the 3 combinations that I had previously found, plus the one in the Olympiad. You...
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Charles Link reacted to renormalize's post in the thread Undergrad Trigonometry problem of interest with
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@Charles Link, given that ##a\geq1,b\geq1##, you can solve your formula ##(a+2b)^2=3(4x^2-a^2)## to get... -
Charles Link replied to the thread Undergrad Trigonometry problem of interest.Very good. That reduces to ## R^2=(a^2+ab+b^2)/3 ##, and is in agreement with my post 24, but far simpler. Thank you @kuruman :)...
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Charles Link reacted to kuruman's post in the thread Undergrad Trigonometry problem of interest with Like.
Using the law of cosines and reasonably simple algebra, I got the following expression for the radius-squared in terms of the given...
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Charles Link replied to the thread Undergrad Trigonometry problem of interest.I took your suggestion, but no luck so far. I had more luck yesterday coming up with the video of post 18 with a search. I'll need to...
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Charles Link reacted to jedishrfu's post in the thread Undergrad Trigonometry problem of interest with Like.
That's an interesting point about knowing numbers. In the movie, The Man Who Knew Infinity, on the life of Ramanujan, there's a scene...
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Charles Link replied to the thread Undergrad Trigonometry problem of interest.@jedishrfu I am pleased with what I got so far on this one. It was my instincts that the integer combinations that would work for this...
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Charles Link reacted to jedishrfu's post in the thread Undergrad Trigonometry problem of interest with Like.
Once you tire of these triplets, you can move onto the Euler brick and then the perfect Euler brick where no one has found a solution...
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Charles Link replied to the thread Undergrad Trigonometry problem of interest.and I found a 4th one that works: 13,31, and 35 (correction =46 instead of 35) with ## x=r=31 ##. Like @jedishrfu said above,( post...
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Charles Link replied to the thread Undergrad Trigonometry problem of interest.I've been trying to find others, but so far only 2,7, and 11 along with 1, 13, and 22 plus multiples thereof. The combinations that...
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Charles Link reacted to jedishrfu's post in the thread Undergrad Trigonometry problem of interest with Like.
Historically, these are likely known triplets for this kind of problem similar to the pythagorean triplets.
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Charles Link reacted to Lnewqban's post in the thread Undergrad Trigonometry problem of interest with Like.
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Charles Link reacted to Lnewqban's post in the thread Undergrad Trigonometry problem of interest with Like.
You are welcome, Charles. Please, take a second look, right triangles are hidden in your diagram: See the Thales' theorem in the...