## Search found 10 matches

Tue Jan 08, 2008 12:51 am UTC
Forum: Mathematics
Topic: Help on an integral...
Replies: 3
Views: 1269

### Re: Help on an integral...

I'm in the midst of making dinner, but for now try this. t = tan(x/2) so sin(x/2) = t / sqrt(1+t 2 ) - do this by right triangle trig so sin(x) = 2t / (1+t 2 ) then dx = 2 dt / (1+t 2 ) See Stewart's calc book - the problems in the section on Strategy for Integration. [Page 505 in the Early Transcen...
Wed Jan 02, 2008 7:37 pm UTC
Forum: Mathematics
Topic: A tricky quartic (for me)
Replies: 22
Views: 2539

### Re: A tricky quartic (for me)

Let x = a2 and use the quadratic formula would be my thought since your equation then reduces to the form ax2+bx+c=0
Tue Jan 01, 2008 6:32 pm UTC
Forum: Mathematics
Topic: Is the Koch Snowflake compact?
Replies: 17
Views: 3248

### Re: Is the Koch Snowflake compact?

Assuming ocean_soul's proof is sound (which it appears to be), we are left with the important lesson about fractals being that although S n is closed for each n, the limiting object is clearly not closed since our snowflake lives in Euclidean space (hence a metric space) and thus would be compact if...
Sun Dec 16, 2007 12:13 am UTC
Forum: Mathematics
Topic: How would you simplify this
Replies: 24
Views: 2343

### Re: How would you simplify this

Q: How would I simplify this?

A: Software (Maple)
Thu Nov 15, 2007 2:24 am UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14289

### Re: Proficiency with LaTeX

I'm usually pretty good at finding Latex help when I need it, but can't seem to find what I need tonight. I'm writing up solutions for a practice exam for my calc class and would like to insert a little L'H directly above the equal sign between two limits. Any quick suggestions? Thanks. Nevermind. F...
Sat Nov 10, 2007 1:41 am UTC
Forum: Mathematics
Topic: What is the smallest number with exactly X distict factors?
Replies: 32
Views: 9897

### Re: What is the smallest number with exactly X distict factors?

Yup, the "figure something out while trying to pay attention to a lecture" method fails again. Oh well. It was a nice problem, that as usual with issues involving primes and number theory is much harder than it appears.
Fri Nov 09, 2007 9:11 pm UTC
Forum: Mathematics
Topic: What is the smallest number with exactly X distict factors?
Replies: 32
Views: 9897

### Re: What is the smallest number with exactly X distict factors?

I will write up a definition and rough justification in a couple hours, but for now, I conjecture that if f(t) is the smallest integer with t unique factors, then some values of f(t) are (computed by hand, so excuse arithmetic errors) f(5) = 2^4 f(6) = 12 f(7) = 2^6 f(8) = 30 f(9) = 36 f(10) = 48 .....
Fri Nov 09, 2007 7:28 pm UTC
Forum: Mathematics
Topic: What is the smallest number with exactly X distict factors?
Replies: 32
Views: 9897

### Re: What is the smallest number with exactly X distict factors?

For an odd number of factors (x) an upper bound is 2 x-1 . Note that for an odd number of factors, the integer n must be a square. 3 factors : 1,2,4 so 2 2 5 factors : 1,2,4,8,16 so 2 4 7 factors : 1,2,4,8,16,32,64 so 2 6 Can anyone find a smaller upper bound? I conjecture that there isn't one, but ...
Fri Nov 02, 2007 1:23 am UTC
Forum: Mathematics
Topic: Correct use of lemma
Replies: 5
Views: 1187

### Re: Correct use of lemma

From a proof writing stand point, Lemma are often used for technical details best left out of the formal proof to minimize clutter and aid the flow of the argument. Additionally, they are often used if there is a result that is not useful enough to be considered a theorem but that is used often. In ...
Mon Oct 01, 2007 4:24 am UTC
Forum: General
Topic: Who the dickens are you?
Replies: 10922
Views: 2416843

### Good evening

Finally decided to get motivated and introduce myself. Hi. For those who care, I ought to be doing some calculus on manifolds homework and then some dynamical systems homework before bed, but decided to read some comics first. I'm a grad student out in the beautiful rocky mountains of the united sta...