Click image, gets bigger.Grrrr ... one person's made a guess about this -- his Spider path is shown in red -- but that ain't the shortest possible path the Spider could take from its corner to the opposite corner. Sorry, but it ain't.
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h2odragon said...
Across the floor to the corner under the end point, then straight up the wall. He could go up the ceiling, but spiders are lazy and why fight gravity if there's no bugs up there.
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Geodesic seems like an overfancy unecessary word for the shortest distance between two points, 'cause the SDB2Ps is always a straight line, right?
Wrong. In a Euclidean 2D plane it's always a staight line, but as you venture beyond the nice neat 2D plane in your geometry textbook into realms which are more like The Real World, you start running into restrictions and conditions which make the SDB2Ps something more complicated than a straight line.
For example, the shortest distance between my backyard and the point opposite it (my Antipode) on the surface of Earth (a wet spot in the Indian Ocean) is a straight line, but am I supposed to dig it? It gets pretty hot as you tunnel through the center of the Earth.
(Thanks to dhpc_raptor for the Latitude & Longitude of Northampton Massachusetts USA. Whoever the #%^&*# dhpc_raptor is, he also folds Proteins@Home [headquartered in France], which is a different project from Folding@Home .)
So for all practical travelling for Real Earth Folks, the SDB2Ps on the Earth's surface is an arc of a Great Circle -- part of a circle, and that ain't a straight line.
That's why you need the fancier word "geodesic." Because Physical Reality just imposes all sorts of difficulties and conditions and restrictions.
In the Spider's case, the restriction is that it must always crawl touching wall, ceiling, floor, or the edges connecting these rectangular planes. (The Spider can't float through air.)
Come on, you can do this. It's not that difficult.
HINT: The fundamental tool you (and the Spider) need is Imagination. That's all. You got to stare real hard at the Problem until The Light Bulb goes on in your head.
10 comments:
I can imagine it, I just can't do the math.
You mean you can figure out the imaginative trick, but you can't compute the length of the spider's path? I'm phoning your geometry teacher and having you recalled.
Yup. It's been a LONG time since I've had to do stuff like this. Navigation in 3D like what we do under water is like this. Remember that we're navigating on a sphere, so straight lines would put us out into space!
somebody wake up RamanuJohn, he's in Maine somewhere. The inability to solve this PizzaQ is an embarrassment to the entire Planet Earth.
I'm not increasing the amount of Pizza reward. This is Not Hard.
Dame RheLynn says she's busy looking after her new baby. (Congrats DRL!)
Abbas, r u there? I know math(s) is icky, but you seem to have the flair for it. we can't talk about Shaving all the time.
grrrrr and i purposely posted this PizzaQ to be EASY!
You don't need imagination for this -- you need the math!
Let's say the spider needs to cross the 20-unit edge, either at a corner or somewhere along the edge. So the spider's distance is the sum of two Pythagorean formulas, each containing "x" to account for the place where the spider traverses the long edge. Find the derivative and solve for 0. "X" equals 10, meaning the spider crosses the 20-unit edge right in the middle. Total distance: 30.54 units. A quick check of any path that traverses the 10- or 13-unit edges shows that any such path is longer than 30.54 units.
I found myself here when googling myself to see if any crazies are talking about me on the internet. I posted a bunch of coordinates when I was awed when Worldwind first came out. I didn't really run proteins at home too long...But it's sure a weird coincidence. Cool that you wrote about me here for some reason anyway.
hey hey hey raptor! oh yeah when I started googling for the Lat and Long of Northampton, I banged into a bunch of your very interesting hobbies and maybe some of your homework. Didn't wanna spook ya so I figured I'd credit you for the Lat & Long, but I'd let you find this when you got around to it. Welcome to Vleeptron!
How's things in your part of Paradise? sup with you? are you at MIT or CalTech yet?
There's another pretty E-Z PizzaQ at
http://vleeptronz.blogspot.com/2008/06/italian-construction-industry-how-far.html
3 slices for the Leaning Tower of Pizza, 1 more slice for the Washington Monument. You choose the pizzeria.
MIT? Not exactly.... I'm a sophomore at Northampton High school. I guess I have more of an internet presence than I thought... Maybe that's a good thing! You are from this area too?
Yup yup, live not far from the high school (Go Blue Devils), so that's why I needed Northampton's Lat & Long.
I guess I shouldn't try to guess ages at the Tri-County Fair, I had you pegged for junior or senior ... but yeah, you're all over the Internet.
you can check out my site (in development) here if you want to
http://dhpc.raptor.googlepages.com/home
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