Portfolio of the week - 2007

[IIC]

Well...first or last for me...there's no in between...lol

[JohnHenry]

unp

Hi Peanuts

Please buy to cover unp...thanks

[IIC]

Well...first or last for me...there's no in between...lol

Guess I was wrong

[Lyehopper]

Scientific farming....

... and here's a picture:



It was not my idea to build the fortress walls in a triangle. Although it does have certain advantages, I tried to get everyone to go for a square shape, which (aside from a circle) produces the maximum square footage per lineal foot of wall built.

For example, say you build 120 lineal feet of palisade wall (which is less than the number of lineal feet actually built in Jamestown, but this is just an example). A triangle with three equal sides of 40 feet each has an area of 692.8 sq. ft., whereas a square with four equal sides of 30 feet each yields 900 sq. ft. Thus you would increase the amount of usable square footage by nearly 30% even though you're building the exact same number of lineal feet of wall. Similarly a rectangle that is 20'x40' yields only 800 sq. ft. A circle with a 120' circumference, though, has an area of about 1,146 sq. ft. Now isn't that the most interesting thing you've heard all day?

Here's one for ya Rockin'Rob....

Outside your 120' circumference fort, you chain a cow (named Lilly) to the circular wall with a 100 foot long rope.... How many square feet of grass can Lilly graze?

Note: When answering bear in mind that as Lilly works her way around the circular wall, the rope will wrap around that circle thus making the outer area of her grazing pattern elliptical and not a true radius.

[Rob]

Here's one for ya Rockin'Rob....

Outside your 120' circumference fort, you chain a cow (named Lilly) to the circular wall with a 100 foot long rope.... How many square feet of grass can Lilly graze?

The answer is: approximately 28,129 sq. ft.

[Karel]

Here's one for ya Rockin'Rob....

Outside your 120' circumference fort, you chain a cow (named Lilly) to the circular wall with a 100 foot long rope.... How many square feet of grass can Lilly graze?

Note: When answering bear in mind that as Lilly works her way around the circular wall, the rope will wrap around that circle thus making the outer area of her grazing pattern elliptical and not a true radius.

There are two ways to approach this problem: the lazy one and the cumbersome one.

In the lazy approach, we assume you are pulling our collective leg, because you know very well that the ground around human habitations usually is so thoroughly trampled, that poor Lilly will not find even one square foot of grass to graze on.

In the cumbersome approach we take this as a mathematical challenge only, and then realize that we don't have the formula for the curiously curved form (at least I don't have it). So here comes an approximation:

The first thing that strikes me is that the circumference given translates to a 38 foot diameter for the fort. That isn't much of a fort, but OK. (I think the Jamestown was about 3 times bigger, but the I'll stick to the measures given by Lye.)

Now the fort obstructs Lilly's movements, so the area she can roam, if not graze, is smaller than a circle with a radius of 100 feet, or about 31,400 square feet.

In this circle the fort itself is excluded, so we subtract as the first obstacle a circle with a radius of 19 feet, or about 1150 square feet. That leaves about 30,250 square feet.

Now for the difficult to visualize boundary that Lily traces as she works her way around the fort and tries to get as far away from it as her tether, wound about the fort, allows. I tried to draw this with a pair of compasses, and found that the area Lilly can't reach looks really small, compared to the 100 foot radius circle. To give an indication: if Lilly is halfway around the fort, she has used up 60 feet of rope, which leaves her 40 feet of freedom. As the diameter of the fort is 38 feet, this means that at that point she still can be 78 feet away from the place were the chain was fixed, so at this point she only gives up 22 feet of range. At a quarter of the circumference, Lilly has 70 feet of freedom, and she is almost 27 feet removed from her "center", so she has only lost three feet range at that point. This means that initially Lilly loses hardly any range, with the loss building up gradually (and accelerating) as she walks around the fort.

Now we have a problem. Lilly, being a cow, would probably keep walkin around the fort until 5/6 of its circumference (when her neck is against the wall), grazing all she could get, and looking wistfully at what she couldn't get. But perhaps we can allow for her getting bored looking at grass she can't get at anyway, and let her find her way back to her starting point, so she can make the circuit in the other direction. What I mean to say is: the problem is symmetrical, and the ranges walking in both directions overlap. So it doesn't get worse than the loss of 22 feet at the point halfway around the fort, and the gradual loss towards those 22 feet. I estimate (looking at my drawing) that the loss would hardly be more than what she loses because of the fort just being in the way, and aiming for a nice round number my estimate becomes 29,000 square feet.

Regards,

Karel

[mimo_100]

The answer is: approximately 28,129 sq. ft.

http://mathforum.org/library/drmath/view/51746.html

[Karel]

http://mathforum.org/library/drmath/view/51746.html

Or rather Goat and silo. We have a relatively longer rope however, which might complicate matters.

Regards,

Karel

[peanuts]

Week 17, last day

Week 17 - Jamestown Settlement
Day 5 - Ok, everything is done- it's time to infest the rest of the new world

Rob takes top honors and gets to make Pocahontas his wife for his expertise in negotiating with the natives, and his supreme knowledge of establishing the settlement.

Skiracer gets to have Ug's sister, Uga- they live happily ever after in a 'peaceful' house

Karel 'steels' third place because of his blacksmithing skills

[peanuts]

Does anyone want to take on the scorekeeping duties starting next week or whenever possible?

I don't know how much longer I can last....

[Karel]

Does anyone want to take on the scorekeeping duties starting next week or whenever possible?

I don't know how much longer I can last....

The POTW is only half the POTW without daily updates, but in a pinch we could do without. That is, in case really nobody steps up to the plate. People with a pinch of accuracy and hopefully some writing skills present? We know you are there!

Regards,

Karel

[Louetta]

The POTW is only half the POTW without daily updates, but in a pinch we could do without. That is, in case really nobody steps up to the plate. People with a pinch of accuracy and hopefully some writing skills present? We know you are there!

Regards,

Karel

If nobody else "steps up to the plate" I will try taking charge of the weekly scorekeeping and try to produce daily reports using my own format with the caveat that if anyone wants to close/open a position in the middle of the day they'll have to give me the prices else accept me trying to eyeball them off a daily Yahoo chart. We will lose the yearly contest and the pretty performance graph.

This will at least salvage the weekly contest. Its not supposed to replace what Peanuts has been doing.

[IIC]

If nobody else "steps up to the plate" I will try taking charge of the weekly scorekeeping and try to produce daily reports using my own format with the caveat that if anyone wants to close/open a position in the middle of the day they'll have to give me the prices else accept me trying to eyeball them off a daily Yahoo chart. We will lose the yearly contest and the pretty performance graph.

This will at least salvage the weekly contest. Its not supposed to replace what Peanuts has been doing.

Well...Just do your best Louetta...it is actually a tough job (I know because I've done it elsewhere)...Thanks for stepping up to the plate...Best, Doug(IIC)

[Louetta]

Well...Just do your best Louetta...it is actually a tough job (I know because I've done it elsewhere)...Thanks for stepping up to the plate...Best, Doug(IIC)

You know...I thought it over. I'm just not going to be able to do it.

I apologize for the confusion. I would have liked to be able to keep things going.

[jiesen]

Congrats Rob, Ski, and Karel on the fine performance last week!

To whom it may concern:
Please start me in $$CASH$$ for next week.

Thanks, Peanuts, for putting forth all of the effort these past months on the contest. I believe I speak for many of us when I say you've really made it fun, and I hope you get a nice break from it and can come back and do it again soon with the same passion.