In the spirit of Top Ten Lists, I've created a top ten list of my favorite equations (or identities) and a little blurb as to why this equation made the list. The list is also counting from 10 to 1 to build up suspense as to what my favorite equation is!! (note: ^ indicates raised to a power)
10. A=(pi)r^2. The area of a circle. I've always loved this equation because of the "pie are not square, they are round" math joke.
9. E=mc^2. Einstein's famous energy equation. It equates mass and energy and is the initials of my husband's name.
8. sin^2(theta) + cos^2(theta) = 1. This is a trigonometric function defining a unit circle. I've always thought it was fun to add sine and cosine. It just seems so wrong, so dirty somehow.
7. y'/y^n +P(x)/y^(n-1) = Q(x) Bernoulli's equation. This equation is a nonlinear differential equation that we used constantly in classes in undergrad. If I had no idea what to do on a problem, I would just write down Bernoulli's equation and a bunch of other stuff and usually got a lot of partial credit. Yea - I'm a great engineer!
6. x =(-b +/- sqrt(b^2 -4ac))/2a Quadratic formula. This is an old standby. Such a great way to solve quadratic equations. Who doesn't love this formula!
5. F=ma. Force = mass times acceleration. Just thinking about this equation makes me think of gravity and I just love gravity. This equation is really all you need to know about physics.
4. F(s) = (integral from 0 to infinity) e^(-st) f(t)dt Laplace Transform. This is another fun equation we used in school. It was really fun because we got to put s's in our differential equations wherever we wanted.
3. F(n) = F(n-1) + F(n-2) Fibonacci sequence. This sequence adds the previous two numbers in the sequence to obtain the current value. This sequence is interesting because the shape of the Nautilus shell follows this sequence as do some flowers. Math in nature - very cool!
2. a^2 + b^2 = c^2 Pythagorean theorem. This is such a great equation to solve for one of the sides of a triangle. One of my greatest math moments is when I realized that 3^2 +4^2 = 5^2. I'm not sure why this was such a math moment, but I remember thinking math was beautiful!
1. e^(i(pi)) = -1. This is actually an identity rather than an equation. However it has all sorts of fun math symbols in it! e is Euler's number, i is an imaginary number - pretty cool, and pi - also a cool number. Tons of irrational numbers together somehow equals negative one. It kind of makes no sense, but on some level it does.
So my faithful readers, are there any I forgot? Are there any you think should have been on here?
I also had to put Sarah's picture with the lamb. She's 11 months old now!!
6 comments:
Would it make me look like too much of a geek if the first thing that I noticed on reading this list was that one of the equations was incomplete? Something about #3 didn't look right to me, so I actually went so far as to Google it just to verify what was missing. I am such a geek.
For the record, here's the completed Fibonacci sequence.
F(n) = 0 for n = 0
F(n) = 1 for n = 1
F(n) = F(n-1) + F(n-2) for n > 1
G = D * A, where G = Gina, D = Dork, and A = the number of atoms in the universe.
Since I didn't really go all that far in math, I believe I've only used 4 of these equations in the past (10, 6, 5, 2). But who knows. It's been a while. :)
Oh, and X = 10. Do I get some prize for solving that complex equation? :)
Thanks for catching my error Tim! You are right the Fibonacci sequence doesn't make sense without the first two numbers of the sequence. Although I think you might be one of the few people who had heard of some of these equations.
Joel - great job solving for x *smile*. J = S*U+AAON which means Joel = Smelly * Ugly + Aggros all of Nektolos.
I myself prefer a more simple equation, such as:
Jenna + Sarah = cute beyond comprehension
Common variable substitutions:
Gina = nerd
Whatchamacallit = kitchen
Prices = braces (you know it G)
Missy = AWESOME
~Anonymous
Here is a great and fun identity that I think you should have on your list. 1 = 2
You never said they had to be true!!
To Start: -1 = -1
-1/1 = 1/-1 write each as a fraction
Take the square root of both sides: sqrt(-1/1) = sqrt(1/-1)
Simplifying: sqrt(-1)/sqrt(1) =- sqrt(1)/sqrt(-1)
In other words, i/1 = 1/i. since the square root of negative one is i.
Multiply both sides by 1/2: i / 2 = 1 / (2i)
Add 3/(2i) to both sides: i/2 + 3/(2i) = 1/(2i) + 3/(2i)
Multiply both sides by i: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) )
Distribute i : (i^2)/2 + 3i/2i = i/2i + 3i/2i
Simplify (-1)/2 + 3/2 = 1/2 + 3/2, since i^2 = -1 and the other i’s end up canceling
Add fractions: 2/2 = 4/2
and this shows that 1=2.
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