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USpapergames
USpapergames
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June 26th, 2020 at 4:25:17 PM permalink
So I just realized something, I think you're going about solving this the wrong way because you're trying to average the volume of all possible rectangle but that's not the question. The average rectangle has the height length equal to the halfway point of 1/16 the circumference.
Last edited by: USpapergames on Jun 26, 2020
USpapergames
USpapergames
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June 27th, 2020 at 2:48:03 PM permalink
So I was actually right about the average area of a rectangle inscribed within a circle! You guys did the wrong question and averaged all possible areas of a rectangle but that's not the question! The average size of the rectangle depends on only 1/16 of the circumstance of the circle.

Here is the solution:

Start by graphing the equation x²+y²=10²
Then draw a line from equation x+y=5 & x+y=-5
The area in between both lines is the answer
5²+5²=10² × the length of both points of either line that contacts the circumference.
7.071 × 18.707 = 132.277

Does that answer look familiar? It does to me because that is the 1st & only answer I have ever given for this problem! Prove my work wrong 🙏
USpapergames
USpapergames
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June 27th, 2020 at 2:57:28 PM permalink
You guys don't realize there is a difference between the average of all the different areas of a rectangle vs the average way a rectangle can be drawn. The rectangle only has 1/16 of the circumference of the circle to be drawn in, so 1/32 of the circle is your median answer since there is no mean randomly drawing inscribed rectangles. Tho I do like the idea of a mean of all potential areas but that is definitely a calculus problem. The hard part was calculating the length of the rectangle, not easy ;)
unJon
unJon
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June 27th, 2020 at 3:06:36 PM permalink
Quote: USpapergames

You guys don't realize there is a difference between the average of all the different areas of a rectangle vs the average way a rectangle can be drawn. The rectangle only has 1/16 of the circumference of the circle to be drawn in, so 1/32 of the circle is your median answer since there is no mean randomly drawing inscribed rectangles. Tho I do like the idea of a mean of all potential areas but that is definitely a calculus problem. The hard part was calculating the length of the rectangle, not easy ;)



But your question was the average area of a random rectangle inscribed in a circle. So we need to know the distribution of all rectangles that can be so inscribed so the average of all those triangles can be taken.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
USpapergames
USpapergames
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June 27th, 2020 at 3:23:12 PM permalink
Quote: unJon

But your question was the average area of a random rectangle inscribed in a circle. So we need to know the distribution of all rectangles that can be so inscribed so the average of all those triangles can be taken.



Think about the question a little harder. A rectangle can only be drawn so many different ways and the average of that must be halfway between all the sizes of the rectangle, not the area! It's obvious you guys aren't that good at word problems. The question says the average area of a rectangle, not all rectangles. Meaning this must be the average rectangle & then find it's area! No wonder nothing you guys were doing made any sense to me!
USpapergames
USpapergames
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June 27th, 2020 at 3:39:36 PM permalink
Literally, everyone is wrong except me because nobody spent any time trying to comprehend the question lol. They all thought it was a mean of all averages problem because they have seen so many similar calculus problems even though I'm shouting up & down that it's not a calculus problem & no trig required but everyone is just ignoring me as if I'm crazy instead of just asking for more information if nothing I was saying made any sense to you. After teaching high school math for 6 years I've learned the worst students are often the brightest but refuse to ask questions for fear of looking stupid.
USpapergames
USpapergames
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June 27th, 2020 at 3:52:26 PM permalink
I checked & there is no translation error from Shackford! The question I have in the description of my video which was posted days before Shackford's AMA is "What is the area of an average rectangle inscribed within a circle with a radius of 10? All corners of the rectangle must touch the circumstance of the circle & not protrude beyond the edge of the circle.

Shackleford's Question: What is the area of a rectangle randomly inscribed in a circle of radius 10?

Again, the rectangle is singular, not plural! Again, everyone is wrong except me, I win🏆. Equations don't lie just like computer simulations! But misinterpretation happens all the time in mathematics, I'm just surprised Shackleford could misinterpret the question even though he clearly posted the right wording of the question. This just goes to show you how easy it is to assume a question that you have solved previously many times. I really did think it had to be the wording of the question for everyone to misinterpret the answer :/
USpapergames
USpapergames
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June 27th, 2020 at 4:08:17 PM permalink
So now that we know the question that we are trying to solve, anyone want to give me an answer for the area of the average rectangular prism inscribed in a sphere with a radius of 10? I promise I won't share the answer for 24 hours :)

P.S. Try to use nothing but pen, paper & a basic calculator, your reliance on technology has stunted your equation skills. Bonus points for whoever gives me the equation & not just an explanation of how they got the correct answer ;)
USpapergames
USpapergames
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June 27th, 2020 at 4:17:07 PM permalink
I think I deserve 2 long island ice teas for having to disprove you guys & prove myself right twice; especially when nobody ever analyzed or attempted to disprove my work!
ThatDonGuy
ThatDonGuy
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June 27th, 2020 at 4:37:11 PM permalink
Quote: USpapergames

Literally, everyone is wrong except me because nobody spent any time trying to comprehend the question lol. They all thought it was a mean of all averages problem because they have seen so many similar calculus problems even though I'm shouting up & down that it's not a calculus problem & no trig required but everyone is just ignoring me as if I'm crazy instead of just asking for more information if nothing I was saying made any sense to you. After teaching high school math for 6 years I've learned the worst students are often the brightest but refuse to ask questions for fear of looking stupid.


Or maybe it's because nobody except you seems to have any idea what the definition of an "average rectangular prism" is. Average as defined in what way?

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