[sunshine]

Wikipedia: Polybius
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[TheBritishInvasion]

I did check that but I couldn't back it up with my textbooks so I wasn't sure if I should trust it, thanks anyway though.

(One of my seminar leaders recently said he was going to put a load of false information on wikipedia, I'm not sure if he was joking)
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[theBSDude]

My cousin's history teacher did that once, to prove a point. Or rather, disprove what many teachers say about Wikipedia being a poor source. He made subtle changes to the dates in an article about the American Civil War, and within ten minutes the dates were fixed.
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[sunshine]

That's why you check the reference links at the bottom, or do a google search. Unless someone else on the forum happens to have a reference source for info on ancient greek historians, that's all any of us are likely to be able to do, after all.
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[TheBritishInvasion]

[Maeniel]

I would recommend looking at some databases. Your school should have purchased some subscriptions; I'm sure that you could get onto a school computer and look up the info you need.
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[Tinalles]

[sunshine]

Yea, I noticed the same lack of a specific time for when he did any of his writings, actually. One article did mention how it's generally thought that he wrote them later in life while staying in Rome to do something of political importance, so I'd suggest going with a general answer like that rather than specific years.
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[TheBritishInvasion]

This isn't actually a homework question, there's a mensa type quiz in one of the newspapers and my mum is attempting it (at work with about 10 other employees) but they're stuck on one of the questions.

A plane is travelling at 495 mph, the return journey is the same distance and it travels at 330 mph.

What is its average speed?

The answer that the staff have come up with is 412.5 mph but the correct answer is 396 mph. My mum wants to know how to get the correct answer.
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[Tenshi]

Does the question give any information about time spent on the ground (at rest), speed of acceleration, or the like?
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[sunshine]

Courtesy my calculus-loving fiance:

assume leg one is 495 miles.
the plane does it in 1 hour
it takes the plane 1.5 hours to do that distance at 330
so, total time is 2.5 hours for 990 (495 + 495) miles
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[Nem]

For any given period of time on the outward journey the distance is 495*T1

Since we know the distances are the same and we have the speeds we can calculate the time of the return journey as a multiple of the first.
495/330=1.5
T2=1.5*T1

Then it's just a matter of plugging in the distances; 495 either way makes for an easy calculation; and dividing by the time it would take to cover that distance. 990 / 2.5 = 396

Edit: Heh, what Sunshine said.
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[TheBritishInvasion]

Thanks to both of you, and thanks to your fiance Sunny. Mum called my dad as well and he came to the same conclusion so she's very pleased that she can stop obsessing about the question now.
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[Nem]

Is it possible to make lines with a common perpendicular intersect? There's this bit where Kant's saying that space is a faculty projection we impose on things - and thus has universal rules for any internally consistent objects that can be imagined knowable before other experiences. One of the rules he advocates is that you can never make two lines with a common perpendicular intersect.

But I was thinking, if space is kinda curved....

Being neither a physicist or a mathematician that was about as far as the thought went. ^_~

I promise not go mad with the revelation and summon vast eldritch abominations while listening to Beethoven and munching on a ham-sandwich if the answer is yes.

As with all people of true evil I prefer Chopin to Beethoven.
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[Tamir]

Sorry, but as far as a mathematical answer to that question goes: depends on your axioms.

Math is really all about making assumptions, and then seeing where those assumptions take you. Under some sets of axioms the answer to your question would be yes, under others it would be no and under others the question would be irrelevant.

In ordinary Cartesian space/Euclidean geometry, which is the most common axiom set when talking about such things, the answer depends on the number of dimensions of the space you're looking at. In two dimensions, two lines with a common perpendicular are either parallel, and thus never intersect, or lie on top of each other and thus intersect at every point. In three or more dimensions, any two lines share at least one common perpendicular, so the answer is yes.

In non-Euclidian geometries, the axiom known as the parallel postulate is replaced. This leads to hyperbolic geometry, where through a single point there can be many lines parallel to a given line, which means the answer to your question is still no (at least in two dimensions). It also leads to elliptic geometry, where the concept of parallel does not exist because every two lines intersect, and so the answer to your question is yes even in two dimensions.

Curved space a la general relativity is a whole different story, and one I don't really know enough about to give you a detailed response.