January 5
Balls in a bag
If i have a bag of balls, containing 3 red balls, 2 blue balls, and 2x10 orange, what is the chance of picking a red ball?
Elementary questions in a plane
I am interested in the two dimensional plane only. Because my questions are elementary at the second year undergraduate level, perhaps somebody could offer pointers of solutions from the existing literatures.
A curve with endpoints is the continuous image of a closed interval. It is easy to prove that a simple curve C with distinct endpoints is homeomorphic to the closed unit interval . Question#1: Is there any homeomorphic automorphism on the plane such that C is carried onto ?
Let A,B be nonempty closed bounded sets in a plane. The distance from a point x to A is denoted by d(x,A). It is easy to prove that the set C of points x with d(x,A)=d(x,B) is a closed set without any interior point. Question#2: Is it a smooth curve? Thank you in advance. Twma 00:53, 5 January 2007 (UTC)
The second question is completely answered. Thanks. For Q1, by homeomorphic automorphism, I mean a homeomorphism from the plane onto itself. Twma 19:33, 5 January 2007 (UTC)
The answer to your question is certainly yes. (In fact there are hugely infinitely many, since at the very least given one you can smush it around -- yay rubber sheets -- to get another.) That doesn't mean I can write down a formula for it, but it certainly exists. In fact, there should be an isotopy of the plane that maps any such curve onto . An isotopy is a homotopy which is a homeomorphism at each moment. This idea, of an isotopy of the ambient space which moves a particular subspace (say a curve) onto another, is called an ambient isotopy, and is the idea of "sameness" that is used to study knots in 3-space. (A better article is here.) Tesseran 16:24, 10 January 2007 (UTC)
symmetry operation in 3 dimensional space
I'm trying to find out what symmetry operation (not an inversion) operates about a point in 3 dimensional space. I've added the table below to clarify what I'm asking for. (Note in the 4d case I've 'assume(d) that all dimensions have to be spatial dimensions.' and orthogonal).
Dimensions (d) 1(number line) 2(plane) 3 (3d space) 4 (?).Inversion in a.. point point point point.Reflection in a.. point (d=0) line (d=1) plane (d=2) 'volume' (d=3)Rotation around a.. impossible point (d=0) line (d=1) (plane (d=2)???)Operation X impossible impossible point (d=0) ...Am I missing something obvious (or is it impossible) (Note I've bracketed rotation about a plane in 4 dimensions since I haven't worked out the maths of it..) 87.102.19.164 01:25, 5 January 2007 (UTC)
Qualifying examination preparation
Hi everyone, I'm in the midst of studying for one of my PhD qualifying examinations, and I've hit a snag on a problem on one of the previous qualifiers; I'm kind of lost as to where to begin. Anyway, here's the statement:
I don't want you to just give me the answer, I'd like a hint or something. Thanks in advance! – King Bee (talk • contribs) 04:08, 5 January 2007 (UTC)
Proving the Viète formula
In the article for the Viète formula a proof is stated which assumes the following identity:
The article also states that the identity can be derived from the double angle identity. How can this be done?--Fiber B 06:15, 5 January 2007 (UTC)
exponents
when and how were exponents first used?
Casting of nines
What properties, behavior and/or history is known about casting of nines. Is the term I know it as proper? I originally learned the trick in gradeschool in Madrid Spain. Very few know of this in the United States. It is an error prone method for checking multiplication.
Example:
2537865 × 4589002 = 11646267560730
Add up the individual term digits until you get a single digit answer, whenever you get an answer of 9 just continue any number +9 "simplifies" to 9, so for example 9 + 5 = 14 = 1 + 4 = 5, you don't have to do this neccessarily, I just think its where the name "casting of 9s" comes from
So you add up the digits of the multiplicand: 2+5+3+7+8+6+5 = 36 = 3+6 = 9 Add up the multiplier: 4+5+8+9+0+0+2 = 28 = 2+8 = 10 = 1+0 = 1
Then you multiply 9 × 1 = 9
If the answers adds up to 9 it is most likely correct.
1+1+6+4+6+2+6+7+5+6+0+7+3+0 = 54 = 5+4 = 9
It is most definetly not foolproof, but for a quick check for doing the multiplication by hand... Haloway13 17:56, 5 January 2007 (UTC)
Approximation of a simple curve by polygonal lines
A polygonal line is obtained by joining consecutive line segments. Let B(e) denote the open disk with center at the origin and radius e>0. Given a SIMPLE curve with dinstinct end points A,B, is it possible to find a SIMPLE polygonal line P with end points A,B such that P is contained in the tube C+B(e)={c+b:c in C, b in B(e)}? The approximation follows easily from uniform continuity but being SIMPLE (injective) is difficult for me to handle. I am interested in plane curves only. Because it is so basic and foundamental, I expect that it is a well known result. Be grateful if somebody could offer me a pointer. Thank you in advance. Twma 19:44, 5 January 2007 (UTC)
What I need is to approximate a bad curve with a nice one. Smooth curves are very nice already. Polygonal lines are the best in my view. Thank you for your help but I am still looking for a better solution. Twma 06:24, 9 January 2007 (UTC)
Value of money in 1800's`
I am trying to find out what the value of 150,000 dollars would have been in the mid 1800's in contrast to what it is worth today. Can you help me? Barb
Equation of a line
The line has coordinates (-5,6) and (6,-7)
What is the equation and how can it be worked out? Thanks in advance81.132.66.73 20:37, 5 January 2007 (UTC)
y = (3/4)x + b2 = (3/4)1 + b2 = (3/4) + b8/4 = (3/4) + b5/4 = by = (3/4)x + (5/4)2 = (3/4)1 + (5/4)2 = (3/4) + (5/4)2 = 8/42 = 2y = (3/4)x + (5/4)8 = (3/4)9 + (5/4)8 = 27/4 + 5/48 = 32/48 = 8Algebra/what is the equation?
If one person can paint a house in 2 days, another person can paint it in 4 days, and a 3rd person can paint it in 6 days, how long would it take the 3 of them to paint it together?
I don't know how to figure this. Please help.
--24.252.201.59 23:12, 5 January 2007 (UTC)--24.252.201.59 23:12, 5 January 2007 (UTC) Deb
Not homework. I have to take a ParaPro test and was just brushing up on a practice test. Can you give me the equation? 24.252.201.59 00:19, 6 January 2007 (UTC)Deb
Thanks!!! 24.252.201.59 01:
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