Here's something random. With everything I'm learning in physics and my classes in general, I decided, "HEY! LET'S DO SOMETHING NERDY BECAUSE I'M THAT AWFUL!"
(And I've barely had any time for myself and I'm all drawn-out right now, and I'm saving that motivation for my drawing class, sorry guys!)
Well first off...
Did you know it's been over a month since I typed a Journal? Yeah, no one really cares. ONTO THE FUN [Lame] STUFF!
Okay, so #2:
What's up with the greatness of "imaginary" numbers? It's not just the fact that they exist, but with the following information...
i = (-1)^(1/2)
e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + (x^5)/5! + ... (so on)
cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + (x^8)/8! + ... (so on)
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + (x^9)/9! + ... (so on)
We can determine...
e^(ix) = 1 + ix - (x^2)/2! - (ix^3)/3! + (x^4)/4! + (ix^5)/5! + ... (so on)
=> e^(ix) = cos(x) + i sin(x)
e^(i*pi) = cos(pi) + i sin (pi) = -1
e^(i*pi) + 1 = 0, which relates the important numbers of e, i, pi, 1, and 0.
You can use this equation to say:
i = e^(i*pi/2)
Now to calculate i^i:
i^i = (e^(i*pi/2))^i
But since circles can repeat as many times as they want to...
i^i = e^(-n*pi/2), where n = 4k + 1
Which means that a simple number like i, when raised to the power of itself, is like hiding infinity in an equation, all because i = (-1)^(1/2).
Did You Know #3:
Horsepower in the British Engineering System (BS, aptly acronymed, and as my physics professor calls it, the "Boneheaded Engineering System") was originally made up by James Watt to sell the steam engine to coal miners prior to the Industrial Revolution?
Did You Know #4:
Isaac Newton invented Calculus, observed the three laws of motion, observed the universal law of gravitation, invented the reflecting telescope, and wrote Optiks in one year, in a barn.
Did You Know #5:
Edmund Halley had to convince Newton to write Philosophae Naturalis Principales Mathematicas (Mathematic Principles of Natural Philosophy), which is now considered the greatest contribution to human knowledge. Prior to the book, the mystery of tides confounded everyone, and Newton solved it in a footnote.
Did You Know #6:
Bournouli printed his infamous "Bournouli's Puzzle" as a challenge to the great Isaac Newton to see if he could solve the problem of getting a bead on a wire from point A to point B in the shortest amount of time. Newton solved it in one night by inventing the Calculus of Variations.
Did You Know #7:
"Rabbit starvation" refers to hikers who would die eating rabbit meat on winter days. No, rabbits aren't lethal to eat, it's just that the energy gained by consuming the rabbit is not nearly enough to compensate for the amount of energy expended catching the rabbit, so you'd die of hypothermia in the winter.
Did You Know #8:
More than 70% of the energy humans consume is expelled in the form of heat, making humans very inefficient at conserving energy for physical activities.
Did You Know #9:
Friction is independent of area of contact and speed of sliding.
Did You Know #10:
Any mass with potential energy needed some type of work to get into its position.
Did You Know #11:
The force in a spring is always opposite to the displacement of the spring or the object it is attached to.
... All of these just came from Physics. Well then.
One last thing...
U is the symbol for Potential Energy.
U stands for... Uhhhhh potential energy.
(Okay, not really, a joke from my professor, but K for Kinetic and W for Work... Hmmm...)
Listening to: ME3 OST - View of Palaven
Drinking: Dr. Pepper