- Jul 29, 2001
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Post your shortcuts for classic problems here... I just felt like doing this cause of the "squares in a square" thread 
Everyone who's taken math through highschool has seen this one, and everyone who's gone on to calc in university has seen it in higher complexity. It's a classic, it can take a while for students learning the material, and now I'm gonna show you how to do it all the way up to an n-dimensional hypervolume... in your head
Problem:
Joe is a farmer. He has property bordering a cliff, and he has 800 feet of fencing to set up a fence. What is the largest area he can enclose using the 800 ft of fencing?
Or, here's the higher order version you do in university:
Jim has a bunch of cardboard and 24 feet of duct tape. He wants to tape up an open-topped box using the cardboard and tape. He must duct-tape the edges of the box where the cardboard is joined. What are the dimensions of the maximum volume of the box?
Crazy-arsed version:
Kodos' hyperdrive is fvcked. Fix it. Make as big a 5th dimensional uber-cube that is open topped in the x and v directions (u, v, x, y, z are your coordinate axes) as you can using 120 inches of duct tape (you didn't know it, but duct tape is hyper dimensional... ).
Yep, you can do all of these in your head. The first one, when learning the material requires setting up an expression for the area, using two sides of length x and the other side of length (800 - 2x), A = x(800 - 2x), A = -2x^2 + 800x, and solving that polynomial for the maximum. Using this method you get x = 200, so you have a 200 x 400 for your dimensions.
I'm not going to actually do the other two problems as they involve using lagrange multipliers, and I'm lazy.
Actually, on second thought, I'm just gonna see if you guys can figure out the method I use for these problems. I'll give hints along the way, but I want to have some fun with this
Everyone who's taken math through highschool has seen this one, and everyone who's gone on to calc in university has seen it in higher complexity. It's a classic, it can take a while for students learning the material, and now I'm gonna show you how to do it all the way up to an n-dimensional hypervolume... in your head
Problem:
Joe is a farmer. He has property bordering a cliff, and he has 800 feet of fencing to set up a fence. What is the largest area he can enclose using the 800 ft of fencing?
Or, here's the higher order version you do in university:
Jim has a bunch of cardboard and 24 feet of duct tape. He wants to tape up an open-topped box using the cardboard and tape. He must duct-tape the edges of the box where the cardboard is joined. What are the dimensions of the maximum volume of the box?
Crazy-arsed version:
Kodos' hyperdrive is fvcked. Fix it. Make as big a 5th dimensional uber-cube that is open topped in the x and v directions (u, v, x, y, z are your coordinate axes) as you can using 120 inches of duct tape (you didn't know it, but duct tape is hyper dimensional...
).Yep, you can do all of these in your head. The first one, when learning the material requires setting up an expression for the area, using two sides of length x and the other side of length (800 - 2x), A = x(800 - 2x), A = -2x^2 + 800x, and solving that polynomial for the maximum. Using this method you get x = 200, so you have a 200 x 400 for your dimensions.
I'm not going to actually do the other two problems as they involve using lagrange multipliers, and I'm lazy.
Actually, on second thought, I'm just gonna see if you guys can figure out the method I use for these problems. I'll give hints along the way, but I want to have some fun with this
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