The Case of the Hungry Spider

Neat challenge. I think the shortest path is one of two; either straight up the wall, across the ceiling and down the other wall, or down the wall, across the floor, and up the opposite wall. Both are 30'. However, there is less chance of getting stepped on across the ceiling.

If you go across the wall it will be about 31+ feet. You can model the two scenarios by unfolding the room's walls onto a flat plane for the 31' scenario. Simple geometry gives you the answer for the path, which is the hypotenuse c^2 = a^2 + b^2.

Dist = sqrt ( (30 * 30) + (8 * 8)

The across the ceiling is simply the sum of the long wall plus the short wall (30').

Close, AH but no cigar. The spider found a couple of paths shorter than 30'. Pretty smart spider, right?

Well, the smartest spider of all would make the fly come to him.

29.732 feet. Two paths.

-e

Euro,

You have found one correct solution, but not the shortest one! I was counting those two paths as one, but you are correct...they are really two different paths. So the spider found two paths of 29.732 and two paths even shorter...a total of four paths shorter than 30'.

Hello JohnV,

You found the shortest path. Good work.

Not yet; we're talking about a spider. The spider dropped to the floor below, then took the above path from the base of the wall to the fly.

Hello Europium,

You got it. Congratulations. Just goes to show man is every bit as intelligent as a spider.

Europium got both solutions right in one statement. Having the spider walk down 1 foot, then then 20 feet along the centerline of the room, and up the remaining 7 seven feet to the fly, is 28 feet, total. Also, having the spider climb the seven feet above his/her/its' starting point, proceeding 20 feet along the centerline of the ceiling, and down the remaining one foot to the fly, is also 28 feet.

However, if the spider could shoot a web-strand accurately enough upwards a distance of the square root of 464, a distance of about 21.54065923 feet, he could then reel the fly in, just like fishing, and not have to walk at all. (Would that be an official category of "fly-fishing"?...)_

I am embarassed to have to correct myself, but I must. While Europium had the most interesting answer(s), it was Annonymous Hero that had the first correct answers, and I offer all due, and appropriate, apologies thereto...

the OP asked what is his shortest path? europium got it first because the others arent the shortest paths.

Right on! Although you have to admire the fly-fishing theory.

Where did you get 7? 10-1=9

I agree with Hero, how can you dispute the math.

But I fear there is more to this then math. Can the spider throw a web? If it can, and I don't know that it can't, how far can it go?

Can the spider walk half way along the ceiling and then lower himself on a web and swing the rest of the way?

I'll be back, I'm going to go ask a spider.

I recall a similar problem. The spider was 1' up from bottom and 1' in from the front on the 10'x10' wall, and the fly was on the other 10'x10' wall 1' down from the top and 1' from the back.

His shortest path walking is 29 feet. He can drop the last foot down the wall with his spinneret.

The spiders wife walked on the web surface and beat him to it by almost 9 feet. she killed him in any case for obvious reasons.

'Funny that a spider thread should come up.

Last night just before we planned to turn in, my wife came shrieking out of the bedroom. A huge spider, she said. It was indeed big. Never seen anything like it. It had very long legs and a smallish body though it was still bigger than any spider I'd ever seen. Not a tarantula. Legs were too long. Maybe four body lengths.

Not a guy to just kill anything that doesn't pose any danger to health or anything, I got a clear plastic jar with the intent of trapping it and setting it free outside. It was on the wall at about my head height.

As I approached it, it flew! It didn't jump. It just stepped off the wall and floated towards me...horizontally! I couldn't see any web from the ceiling which seemed to be the only way how it can move like that.

Anyway, I was so surprised I stepped back. It landed about two feet in front of me. Next thing I knew, my wife had smashed it with a slipper!

• Tinsy winsy spider went up the wall at home.
• Vulcan tried to trap it and set it free alone.
• Down came the spider flying down his web
• And his life ended with a slipper on his head

good one!

I've seen this phenomena before. The spider actually casts out some silk and uses it like a hang glider or parachute. Amazing creatures.

Sound like the behavior of the Brown Recluse Spider.

Nasty little buggers!

No, I've been looking in the web, or rather, internet , and I think it may be a type of wolf spider. I couldn't find a picture that looks close enough though. If I ever find one, I'll post it. Who knows, if another one shows up, I'll take its picture before my wife gets to it.

Wolf spiders are not uncommon in California.......experience shows they can jump horiz. about three feet.

MR. GUY

But, I heard the fly flew away before the spider got there.

Impossible!! Have you no idea of spider silk strength? It is extraordinarily strong. Once a simple creature such as a fly is "loomed", then it is most assuredly "doomed".

In memoriam:

Itsy bitsy spider went up the shortest path

Along came the wife and knocked the spider out

Out came the man and took away the wife

Itsy bitsy spider then came back to life

Without looking at others' postings, I make it 30', straight up (9'), straight along (20'), straight down (1').

Checked for a shorter route going across to the side wall to a point x' above floor, along side wall to a x' below ceiling (by symmetry), then to the fly. I make minimum distance by that route when x = 2' 4" which sounds reasonable but gives total length just over 31'.

Perhaps I'm missing something, I'll look at thread now....Codey