/sci/ - Science & Math

>>3533151
You'd have to wait 40 minutes minimum to see the effects of the blast on earth. Your dream is a farce!

>>3396436
Thanks.

Fixed

OC

>>3395760
Notice that <span class="math"> dx [/spoiler] is infinitesimal and it's being added infinitely many times during a time period <span class="math"> t [/spoiler], which results (when velocity is constant in this case) in a well defined finite answer <span class="math"> v t [/spoiler]
<span class="math"> x(t)=\int_{0}^{t}dx = \int_{0}^{t} \frac{dx}{dt} dt=\int_{0}^{t} v dt= v t [/spoiler]

>Why exactly did scientists believe in the Planck length
The Planck length isn't really pinned down to anything experimentally confirmed in physics right now, it just arises from dimensional analysis of physical constants.

>obviously you can get smaller distances, space is infinitely divisible, math tells us this, and it's a priori obvious.
No it's not. It's only obvious in complete metric spaces.

>You can't actually solve those old greek paradoxes involving reaching a door, since you have to reach half the distance before you reach the door and half of half the distance and so forth, forever...you can't traverse infinite distances
Yes you can, Calculus shows us how doing an infinite amount of infinitesimal things in a finite time can happen.

>Even if there was some magical "smallest distance" set by God (this would only work in a theistic world not a natural-logical one) you wouldn't be able to find it out and you could still abstract it into two parts, and thus half it, and then half that...there is no such thing as a "one" unit in reality, we just imagine lines and limits...
...and Grahams number doesn't fit in the universe, so what? Physical laws don't prevent us from doing abstract math.

http://en.wikipedia.org/wiki/Cyclotron

>>3393136
If your doing this under AQA like I did make sure you really fill in all the paperwork (Record of Marks, Record of initial planning, Mid-project review etc) it's worth a lot of marks. Wave all the material which should get marks right under the examiners nose. Also make a lengthy production log and get a load of citations (doesn't matter where from, make them up if needed). My bibliography wasn't long enough because I didn't lie about it and I lost marks for it. Also follow a established citation system (Harvard or footnote)

Make sure you layout your objective from the beginning and then confirm that you've done it or not by the end. I got lost in the science and didn't really set up any concrete objectives. From what I can see from your planning, you will not be able to present anything as your a final collective piece to show that you have achieved your objective. I, like I presume you will, argued that the knowledge and understanding gained was the objective fulfilled - although my mentor for the project didn't like this.

You are planning an informative piece of literature, which is not what a EPQ is about. Extended Project Qualification - means that it must be a project, so in your case the project would be to research gravity, your documentation would be how you did the research and the final piece would be the informative literature you are planning. Make sure you don't just write about gravity and then get no marks for writing about the project.

>>3393048
A*

>>3392785
http://www.mediafire.com/?cr5lu046tz09rbq
Hope it helps.

I did a similar project on gravity while in "high school".

"...." - Grigori Perelman

No.
>So, there can't be such a thing as moving a meter because you can start from 0m and try to reach 1m by incremental steps, but since incremental steps can have an infinite amount of places to them you would never reach 1m ever. It would be impossible, right?
http://en.wikipedia.org/wiki/Supertask#Motion

Furthermore when constructing the real line the natural numbers are defined first by induction, then later the rational and whole real line emerges.

Yes. Not in the quaint way of geometric symmetry though.

http://en.wikipedia.org/wiki/Symmetry_%28physics%29

Sorry, bit off topic;
>taking a gap year
Why? You do realize your tuition fee's will be at least doubled.

http://lichess.org/26rvay65

>>3310523
Come at me bro's.

http://lichess.org/x78t0glg

http://www.wolframalpha.com/input/?i=volume+of+universe+%2F+planck+volume

>>3307017
Because if everyone shared this idea then the world would be far better than the drug induced stupor you describe.

>>3306719
"Until you have done something for humanity, you should be ashamed to die" - Horace Mann

Neither.

It means your <span class="math"> gay^{2} [/spoiler]

All holomorphic functions can have a domain of the entire complex plane which has a range of the entire complex plane (minus one point in some circumstances). You need to state a range, then we can work out the domain.

If you want to restrict the range and domain to just the real numbers then;
<span class="math"> x \leq -2 [/spoiler] and <span class="math"> x \geq 2 [/spoiler]

Familiarize yourself with Hamiltonian, Lagrangian principles and Noether's theorem, and you should be fine for QM.

This is not the required proof for the last question, but it just popped into my head and gives a lower boundary. No knowledge of Taylor series required.

When <span class="math"> n > 3 [/spoiler] we know that <span class="math"> \frac{1}{n!}<\frac{1}{2^{n}} [/spoiler]. Therefore
<span class="math"> \sum_{n=4}^{\infty }\frac{1}{2^{n}}>\sum_{n=4}^{\infty }\frac{1}{n!} [/spoiler]

<span class="math">\sum_{n=1}^{\infty }\frac{1}{2^{n}}=1[/spoiler]
Therefore
<span class="math"> \sum_{n=4}^{\infty }\frac{1}{2^{n}}=\frac{1}{8} [/spoiler]

Expanding the first 3 terms gives
<span class="math"> \sum_{n=1}^{\infty }\frac{1}{n!}=\frac{5}{3}+\sum_{n=4}^{\infty }\frac{1}{n!} [/spoiler]
Therefore
<span class="math"> \sum_{n=1}^{\infty }\frac{1}{n!}<\frac{43}{24} [/spoiler]