A man walks into a garden. He sees a circular sidewalk in that garden.
In the interior of that circular sidewalk is a tree.
On that tree is a squirrel.
The man does not see the squirrel because the squirrel is on the opposite side of the tree from the man.
The man walks to the circular sidewalk, and onto the circular sidewalk.
As the man walks around the tree, on the circular sidewalk, the squirrel scampers around the tree so as to always remain on the opposite side of the tree from the man.
So even though the man studies the tree as he walks around it, he never sees the squirrel.
A man walks into a garden. He sees a circular sidewalk in that garden.
In the interior of that circular sidewalk is a tree.
On that tree is a squirrel.
The man does not see the squirrel because the squirrel is on the opposite side of the tree from the man.
The man walks to the circular sidewalk, and onto the circular sidewalk.
As the man walks around the tree, on the circular sidewalk, the squirrel scampers around the tree so as to always remain on the opposite side of the tree from the man.
So even though the man studies the tree as he walks around it, he never sees the squirrel.
And I suppose yes, to the second, unless you're an empirical solipsist, many of whom seem to populate this board. (Sic.)
"Mad" Miles
:burngrnbounce:
P.S. I was good at, and enjoyed, geometry. I didn't like algebra, too much rote memorization without a connection to anything I thought of as real, although I liked learning new concepts.
Only at the end of Advanced Math / Trigonometry (all this in Jr. High and High School) did I realize that I'd been royally screwed by my teachers, when I looked in the back of the book and saw the conic sections.
I've been telling math teachers ever since to show us visual learners those drawings at the beginning of Algebra I, or at least at the beginning of Algebra II, instead of just introducing and enforcing compliance with dry formulae (aka "functions").
Frederick M. Dolan
01-14-2008, 08:48 PM
The man and the squirrel orbited a common center.
He was a squirrely man.
Yes. To the first question.
And I suppose yes, to the second, unless you're an empirical solipsist, many of whom seem to populate this board. (Sic.)
"Mad" Miles
:burngrnbounce:
P.S. I was good at, and enjoyed, geometry. I didn't like algebra, too much rote memorization without a connection to anything I thought of as real, although I liked learning new concepts.
Only at the end of Advanced Math / Trigonometry (all this in Jr. High and High School) did I realize that I'd been royally screwed by my teachers, when I looked in the back of the book and saw the conic sections.
I've been telling math teachers ever since to show us visual learners those drawings at the beginning of Algebra I, or at least at the beginning of Algebra II, instead of just introducing and enforcing compliance with dry formulae (aka "functions").
alanora
01-14-2008, 08:54 PM
We are not given enough information to determine if the squirrel was manly. me
The man and the squirrel orbited a common center.
He was a squirrely man.
MsTerry
01-14-2008, 09:28 PM
Neither man nor Squirrel moved.
It is the tree that is rotating
Here is the setup.
A man walks into a garden. He sees a circular sidewalk in that garden.
In the interior of that circular sidewalk is a tree.
On that tree is a squirrel.
The man does not see the squirrel because the squirrel is on the opposite side of the tree from the man.
The man walks to the circular sidewalk, and onto the circular sidewalk.
As the man walks around the tree, on the circular sidewalk, the squirrel scampers around the tree so as to always remain on the opposite side of the tree from the man.
So even though the man studies the tree as he walks around it, he never sees the squirrel.
Neither man nor Squirrel moved.
It is the tree that is rotating
At the still point of the turning world.
Valley Oak
01-16-2008, 12:40 AM
Is the fact that the squirrel was closer to the center than the man have any relevance?
I visualize the movement of planets rotating around each other when I think of this riddle.
So neither the man nor the squirrel orbited around each other. They simply shared the same center like moons around a larger planet?
Edward
The man and the squirrel orbited a common center.
He was a squirrely man.
Hummingbear
01-16-2008, 09:44 PM
Did the man walk around the squirrel?
Depends on the realm in which you define "around."
Seen as a problem in plane geometry, the man's path surrounds the squirrel's path, so he must have gone "around" him--we assume.
But the problem was not posited on a plane, but in three dimensions, which would require a much more thorough treatment of "around."
Likely, the tree is taller than the man. Plausibly, the squirrel's path remained higher off the ground than the man. So from a point of view of, say, another human outside the circle, the man's path is (approximately) a hollow cylinder bound on one end by the ground and on the other end by the height of his head; the squirrel's path is a completely separate shape (perhaps a bit twisted) in a different plane. A line through the centers of the two cylinders would be perpendicular to the ground, but they don't have the same center (unless the squirrel ran around the tree at a very low height), so there is no plane, much less a space, in which the man's path surrounds that of the squirrel.
Okay, guys, get back in the box now, but only if you really want to.