T. Rev (

st_rev) wrote,
2005-10-25 11:11:00

Hilarious Math III

I am bored. Here is something to do for you and me:

Ask me a question. Math questions would be best here, but other questions are OK too. I will give an answer that is either mathematically correct, or funny, or I will post a picture of a baby monkey.

Tags: hilarious math

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91 comments

October 25 2005, 15:52:08 UTC 6 years ago

Ok, non-Euclidian geometry. What's up with that.

October 25 2005, 16:04:16 UTC 6 years ago

Well, Euclidean geometry has its roots in surveying and construction. The basic objects in Euclidean geometry are the point, the line and the plane, and these are idealizations of place, straight path and flat surface, respectively. The importance of place is obvious, and straight paths arise as lines of sight, among other things.

Euclidean geometry's axiomatic approach was astonishingly successful; really, this was pretty much the first time the human species had ever gotten pure abstraction right. Of course, there were lots of curved paths in the world, too, and surfaces that weren't flat. It turns out that you can develop a geometry of curved surfaces, it's just harder and requires more sophisticated techniques, a lot of which had to be borrowed from later subjects like calculus. And that's what 'non-Euclidean' geometry is: the geometry of stuff that isn't flat.

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simon_draskovic

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October 25 2005, 16:50:09 UTC 6 years ago

Why is it that we never learn a single proof until the 10th grade?

Is it really better to just memorize the theorums, or to actually learn the hows and the whys.

In other words: Why is math made boring?

October 25 2005, 18:03:43 UTC 6 years ago

Math is made boring because most math teachers hate, fear, and do not understand mathematics, and were taught by teachers who hated, feared, and did not understand mathematics, yea, unto the seventh generation or whenever it was that Sputnik launched and frightened the country into thinking we needed to make every child into an engineer.

I prefer the old British system: Latin, Euclid and the Bible. They conquered half the world with that crap, despite the fact that Latin, Euclid and the Bible are completely useless.

October 25 2005, 16:56:37 UTC 6 years ago

What do you think? P=NP?

-R

October 25 2005, 18:05:09 UTC 6 years ago

BABY MONKEY

mothwentbad

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mothwentbad

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October 25 2005, 17:02:55 UTC 6 years ago

Three baby monkeys
Jumping on the bed
One fell off and bumped his head

How many baby monkeys are left? (please show your work and pictures of the monkeys)

October 25 2005, 18:20:41 UTC 6 years ago

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el_christador

October 25 2005, 17:19:32 UTC 6 years ago

Discurse on Galois theory, please.

October 25 2005, 18:22:54 UTC 6 years ago

Fuck Galois theory, that Galois theory ain't nothin but a ho.

(Or did you mean discourse?)

el_christador

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October 25 2005, 18:33:24 UTC 6 years ago

What does it mean if you dream about a baby monkey pestering you in a mall?

October 25 2005, 18:35:57 UTC 6 years ago

October 25 2005, 19:04:53 UTC 6 years ago

How is the universe infinite, and how is there no beginning or end to time, and most importanly, what makes us think we know such things?

October 25 2005, 19:07:33 UTC 6 years ago

It isn't, there is, and we don't, where by 'we' I mean 'me'. I don't know how the hell other people justify it.

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October 25 2005, 19:28:35 UTC 6 years ago

That is actually kind of complicated! If G is abelian, of course, RG is commutative, of course. The subring R.Z(G) is central, and the sum of the group elements is also always central. In general, though, RG decomposes as a direct sum of matrix algebras and determining the centers can be tricky (i.e. I don't know the full answer off the top of my head).

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October 25 2005, 20:07:43 UTC 6 years ago

How many roads must a man walk down?

Also, where have all the flowers gone?

October 25 2005, 20:11:27 UTC 6 years ago

a)

b)

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October 25 2005, 20:51:29 UTC 6 years ago

What's up with functionals and eigenvalues? That's about the point where I gave up on the math minor, I just could never get a good intuition about those. (Plus I wanted to take the class on Gödel's theorem, which wasn't required, instead of the boring-looking class on computation, which was required.)

October 25 2005, 21:01:53 UTC 6 years ago

BABY MONKEY

October 27 2005, 01:17:16 UTC 6 years ago

I want to construct a five-pointed star with only a compass, unmarked straightedge, and pencil. And paper. Because I have to summon the devil. On the paper. Soon. Can you help me?

October 27 2005, 01:24:49 UTC 6 years ago

I will assume that you want a regular five-pointed star, and not an arbitrary one, for which a straightedge suffices.

First, construct a regular pentagon. To construct the regular pentagon, start with a circle with center O. Draw a diameter AOB, and draw the perpendicular bisector COD. Find the midpoint E of AO. With E as center, draw an arc with radius EC, intersecting the segment OB at F. Set your compass with radius CF. Now with center C, draw an arc intersecting circle O at G and J. With center G, draw an arc intersecting circle O at C and H. With center J, draw an arc intersecting circle O at C and I. Then connect C to G to H to I to J to C with line segments. CGHIJ is the regular pentagon, and side HI is parallel to the diameter AOB. If the radius of the circle
is r, then the side of the regular pentagon is r*sqrt[(5-sqrt[5])/2].

Once you have the regular pentagon drawn, you may either connect the vertices in the form of an inscribed pentagram, or you may extend the edges outward using the straightedge until they intersect.

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caroleotter

October 27 2005, 01:19:35 UTC 6 years ago

i

What do imaginary numbers *mean*? Of course, i is the square root of -1, but why should we care?

I should mention that I was a physics major in college, but I barely passed. They used complex numbers when we did wave mechanics, but I never understood why.

October 27 2005, 01:46:42 UTC 6 years ago

Re: i

The most honest answer I can give you is that i is the square root of -1! Why care? Well, sometimes you just want to be able to solve x² + 1 = 0.

I can't tell you what i apples look like, but then again I can't tell you what -2 apples look like, either. The thing is, sort of like with negative numbers (which were another technical innovation people were uncomfortable with when they were introduced) if you treat i consistently as if it were a number, and throw it into the mix with the real numbers, you get a new, different, but self-consistent system of, well, numbers--the complex numbers.

Now, two of the most important classes of functions in applied math are the exponential functions and the trigonometric functions. These seem to be very different--the exponential functions blow up or decay to nothing in a nice, steady way, while the trig functions oscillate forever. But from the viewpoint of complex numbers, it turns out that they're the same thing, because of the famous formula

e^{i theta} = cos(theta) + i sin(theta).

Among other things, this means that you can treat the growth or decay of wave and its frequency at the same time in a unified context.

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October 28 2005, 01:45:36 UTC 6 years ago

The uncountability of the irrational numbers

Ok, you finally drew me out on this.

You know that proof that the irrational numbers are uncountably infinite, or of aleph-1 cardinality, or whatever? Anyway, the idea is you posit a list of irrational numbers, then construct a new number by going diagonally through the list, taking subsequent digits from subsequent numbers; then add 1 modulo 10 to each digit; the resulting number is irrational and not in the list? The resultant is obviously not in the original list. But sometimes I disbelieve that the constructed number is necessarily irrational. How do you know that your resultant was not changed by your procedure into a non-irrational number? I guess the idea is that the resultant is not repeating, therefore irrational, but I have trouble believing it sometimes. The substitution procedure doesn't seem to guarantee a non-repeating decimal.

October 28 2005, 04:00:04 UTC 6 years ago

Re: The uncountability of the irrational numbers

Actually, the proof is a bit different, and simpler.

That proof shows that the real numbers are uncountable. That's the irrationals and the rationals taken together. So there's no need to show that the resulting new number is irrational; it could be either. Doesn't matter.

(The rationals are countable, so they're a vanishingly small part of the whole set of real numbers, which means the irrationals are uncountable. But that's a corollary.)

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October 29 2005, 02:27:41 UTC 6 years ago

Eh, it's convenient to have. Rejecting it generally means an enormous amount of extra irritation.

Of course, if you only ever deal with finite or countable objects, it's pretty much irrelevant.

clearvariant

October 30 2005, 18:40:38 UTC 6 years ago

Analysis is the worst and most boring of all fields of mathematics. Prove, or provide a counterexample.

October 30 2005, 19:06:11 UTC 6 years ago

I think it's tied with logic for that.

November 1 2005, 21:05:22 UTC 6 years ago

What subject matter do you find most interesting in mathematics? Do you know much about mathematical physics?

November 1 2005, 23:49:39 UTC 6 years ago

I am an algebraist by training. I like algebra and topology best.

I don't know much about mathematical physics. I wish I did, but I am terrible at physics and have forgotten most of what I used to know.

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91 comments

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