lithiumdeuteride

Here's the brainteaser:

Does there exist a purely mechanical system which, when load P is applied to it, experiences a stress with a magnitude of S, but when a load 2P is applied to it, experiences a stress with a magnitude less than S? If so, describe that system.

Note: The load is doubled, and its direction is unchanged. The mechanical system must of course have a nonlinear response. If its response were linear, the stress would be exactly 2S. Any type of mechanism may be employed, but the system must be in static equilibrium at load P, and also at load 2P. A dynamical system is considered cheating.

To restate the problem:

load P --> stress S in static equilibrium

load 2P --> stress less than S, but greater than 0, in static equilibrium

Describe the system and how it achieves such non-linearity.

I realize this sort of question has been asked before, but I'm looking for a certain kind of epic classical music.

Pieces I would place into this category are:

* Wagner's Prelude from Lohengrin

* Rachmaninoff's 2nd Piano Concerto, first movement

* Verdi's "Dies Irae"

* Saint-Saëns' Organ Symphony, last movement

* Beethoven's 5th symphony, first movement

* Holst's "Jupiter"

* Vivaldi's "Et in Terra Pax"

I would describe these pieces as having the following qualities:

* Loud

* Strong melody

* Catchy chord progression

* Steady tempo (not necessarily throughout, but where it counts)

If anyone could suggest more musical selections of similar qualities, I would be grateful.

No, I don't mean the Rachel Carson book.

I'm referring to the feeling I (and perhaps you) get when I listen to some really profound statement about science. Carl Sagan and Richard Feynman were especially good at these kinds of statements. For those of you who don't know what I'm talking about, watch this:

http://www.youtube.com/watch?v=myPSkL_S45E

I am not religious, but my question is for religious and non-religious, for scientists and non-scientists:

Do you think that the feelings I described are the same as those felt by religious people when praying to or contemplating their respective deities, or when listening to religious texts being spoken or sung? It seems to me that there is much in common; that the same brain functions are used in each of these experiences. In other words, might not they be the same experience, but in different contexts?

What are your thoughts?

I have asked this question in both the Religion and Science sections, to get a broader perspective.

No, I don't mean the Rachel Carson book.

I'm referring to the feeling I (and perhaps you) get when I listen to some really profound statement about science. Carl Sagan and Richard Feynman were especially good at these kinds of statements. For those of you who don't know what I'm talking about, watch this:

http://www.youtube.com/watch?v=myPSkL_S45E

I am not religious, but my question is for religious and non-religious, for scientists and non-scientists:

Do you think that the feelings I described are the same as those felt by religious people when praying to or contemplating their respective deities, or when listening to religious texts being spoken or sung? It seems to me that there is much in common; that the same brain functions are used in each of these experiences. In other words, might not they be the same experience, but in different contexts?

What are your thoughts?

I have asked this question in both the Religion and Science sections, to get a broader perspective.

The words "debt" and "debit" are similar in meaning, and in spelling. Is this just a lingual example of convergent evolution (by which I mean two words circuitously arrive at similar spellings despite different roots), or do the words have the same root?

Furthermore, what are their roots?

Suppose we have a triangle with sides x1, x2, and x3. At each vertex of the triangle lie point masses m1, m2, and m3. Mass m1 is at the vertex opposed from side x1, and m2 and m3 are similarly placed.

Now we consider the center of mass of the system, wherever it might be. We draw lines from m1, m2, and m3 to this center of mass. These lines have lengths r1, r2, and r3.

Your task:

Find r1, r2, and r3 as algebraic functions of x1, x2, x3, m1, m2, and m3...

...and do so without referencing any coordinate system not native to the triangle! Use ONLY trigonometric arguments. You are allowed to construct other triangles within the main triangle.

This is a question for anyone who makes their questions and answers private. If you are one of these people, what is your motivation for doing so? I don't understand why anyone would want to prevent people from reading their past responses.

My thinking is this: If I made sensible replies, I'd have no reason to hide them. If I made only vulgar and insulting posts, I wouldn't care who read them, since my purpose is clearly to insult (that is, I would not be ashamed).

I can't come up with a logical motivation to hide my answers, yet many people make theirs private. Help me understand this phenomenon.

Warning: Not for the faint of heart.

I have a right triangle with a hypotenuse of length 4. I connect the triangle's incenter, hypotenuse midpoint, and right-angled vertex with three line segments, forming a smaller triangle within the main triangle.

What is the smallest of the three angles of the main triangle when the smaller triangle's area is maximized? Additionally, what is the maximized area of this smaller triangle?

It is around 20 degrees, but I'm looking for exact algebraic solutions.

Does anyone know the exact playlist shuffling algorithm that Winamp uses? Is it the Knuth shuffle, or something else?

Additionally, what pseudo-random number generator does it use? Mersenne twister, linear feedback register, Blum Blum Shub, or what?

Here's a challenge problem I thought up relating to interstellar travel at relativistic speeds.

Your spaceship is in Earth orbit. You want to journey to Proxima Centauri, which is 4.22 light-years away, then return to Earth. Your ship is capable of traveling at any speed between 0 and c, the speed of light. If you make the journey at close to the speed of light, time dilation will cause many years to pass back on Earth. However, if you travel extremely slowly, the trip will take a long time.

What fraction of the speed of light do you travel to minimize the amount of time that passes on Earth during your round trip to Proxima Centauri?

10 points to the first correct answer!

My dog, a labrador-ish thing, goes absolutely nuts when I start playing the piano. He howls as if it he was being tortured horribly. However, when I play a recording of a piano, he does not react.

Can anyone offer an explanation for this? I'm mystified.

Here are some number sequences I thought up. See if you can find the next number, and also identify the pattern.

Sequence 1:

1, 3, 4, 7, 6, 12, 8, 15, 13, ?

Sequence 2:

100, 19, 83, 34, 70, 45, ?

Sequence 3:

1, 1, 0, -1, 0, 7, 28, 79, 192, ?

Sequence 4:

2, 5, 10, 17, 28, 41, 58, 77, 100, ?

The numbers in the sequence may or may not depend on the previous number.