User:Guardian of Light
From Wikipedia, the free encyclopedia
User at Wikipedia.
Contents |
[edit] Major Contributions
Some pages I've invested a lot in:
- Differentiable manifold
- Proofs of Fermat's little theorem
- John Derbyshire
- Ayla (Chrono Trigger)
- Frog (Chrono Trigger)
- Sonic Heroes
[edit] Minor Contributions
[edit] Mathematical
- Trigonometric function
- Hyperbolic function
- Taylor series
- Taylor's theorem
- Table of integrals
- Derivative
- Partial fraction
- Metamathematics
- Coversine
- Critical line theorem
- Fermat's little theorem
- Limit (mathematics)
- Domain (mathematics)
- Laplace transform
- 173 (number)
- Amortization (business)
[edit] Scientific
[edit] Miscellaneous
- Chrono Trigger
- Melchior (Chrono Trigger)
- English Language
- Crono
- Serge (Chrono Cross)
- Kid (Chrono Cross)
- Lynx (Chrono Cross)
- Luccia
- Harle
[edit] Creations
The pages I myself have made (from ye olde scratch) are--in chronological order:
[edit] Problems
To show the probability that two integers chosen at random are relatively prime is 
.
Proof: It is sufficient to show 
. When we have a polynomial with constant term one, we may rewrite it in factored form as follows: If 
are the roots of a polynomial p(x), then we may write 
.
Now examine the power series for the function sin(x)/x. 
Well we also know we can rewrite sin(x)/x in terms of its roots to be:
If we examine the quadratic term in each we find that:
