# Nerdy Dopers: What equations are permanently burned into your brain?

F = ma (force = mass * acceleration) has been burned into my head since high school physics.

PV = nRT. I’ve used this chemistry just once since learning it in school. Yet I can’t get it out of my head.

V = IR. I’m an EE, so this goes without saying.

V = (4/3)πr[sup]3[/sup]. This is the volume of a sphere as a function of radius. I’m not sure why this equation has been stuck in my head all these years.

Ever since grade eleven: the quadratic equation. We were told to go over this many many times in our heads.

“x equals negative b plus or minus the square root of b squared minus 4 a c all over 2 a”

Over and over. Until we could recite it in two seconds.

All of yours, plus:

**V = at

X = Vt + 1/2at[sup]2[/sup]

CO = HR * SV **( cardiac output is stroke volume times the heart rate.)

MAP = CO*SVR (mean arterial pressure. SVR is systemic vascular resistance. Technically, MAP is (CO*SVR)+CVP, where CVP is central venous pressure, but CVP is generally so low compared to MAP that it is ignored.)

There are also several constants I got stuck in the ol’ noggin:

c = 3.010[sup]8[/sup]m/s
n = 6.022
10[sup]23[/sup]
e = 1.6*10[sup]-19[/sup] J
(or 1 eV)

Most of the above and though while not quite equations as such:

S = O/H
C = A/H
T = O/A

From Logic class:

NOT(A OR B) = NOT A AND NOT B (aka: break the line - change the sign :o ***** )
***** There is no correct smiley for this, read as <<embarrassed grimace>>

Newton’s:

s = ut + 0.5ft2
v
2 = u*2 + 2fs

Euler’s:

E**(PI)i + 1 = 0 (I don’t know anything about it though!)

Pythagoras:

a(hypotenuse)2 = b2 + c**2

Chess conversion:

English**8 + 600 = ELO

f = ma, e = iz, s = at[sup]2[/sup]/2, V = at, KE = mv[sup]2[/sup]/2, and so on

and, although not an equation, for some reason I have trouble remembering where I put my glasses but I have no trouble with

Avogadro’s Number and I don’t even like chemistry.

F = ma

D = m/v

Gah, I’m bloody worthless: I know so much that I use so little, I might just as well know nothing at all. But…

Aside from the usual geometric identities, here are the fun ones.

Euler’s Identity:

e[sup]jθ[/sup]= jsin θ + cos θ

and the special, beautiful case of:

e[sup]jπ[/sup] + 1 = 0
Exponental series:

e[sup]x[/sup] = 1 + x/1! + x[sup]2[/sup]/2! + x[sup]2[/sup]/3! + . . .
Maclaurin Expansion:

f(x) = f(0) + x f’(0)/1! + x[sup]2[/sup] f’’(0)/2! + x[sup]3[/sup] f’’’(x)/3! + . . .
The sine and cosine series[sup]1[/sup]:

sin x = x - x[sup]3[/sup]/3! + x[sup]5[/sup]/5! - x[sup]7[/sup]/7! + . . .

and

cos x = 1 - x[sup]2[/sup]/2! + x[sup]4[/sup]/4! - x[sup]6[/sup]/6! + . . .
ODE for 1D linear damped vibrations:

**d[sup]2[/sup]y/dx[sup]2[/sup] + 2b dy/dx + a[sup]2[/sup]y = 0 **

and its associated solutions. (Like I’ll ever use that again, but after three courses of linear systems/vibrations/classical controls it won’t go away. :rolleyes: )
The Laplace Integral:

L[f(t)] = int(0, inf) e[sup]-st[/sup]f(t) dt (too lazy to figure out the coding for the integral sign, and vCode doesn’t like the infinity symbol, I guess.)
and more mundane,
Moment of Inertia for a rectangle:

I[sub]x[/sub] = ab[sup]3[/sup]/12
The Parallel Axis Theorem:

I[sub]x[/sub] = I[sub]0[/sub] + x[sub]0[/sub][sup]2[/sup]m
Stress Due to Bending (Outer Fiber):

σ[sub]x[/sub] = M[sub]x[/sub]b/I[sub]x[/sub]
Period of a Simple Pendulum:

τ = 2π √(l/g)
Bernoulli’s Equation:

p[sub]1[/sub]/γ + V[sub]1[/sub][sup]2[/sup]/2g + z[sub]1[/sub] = p[sub]2[/sub]/γ + V[sub]2[/sub][sup]2[/sup]/2g + z[sub]2[/sub]
and the always useful Ideal Gas Equation:

PV = nRT
I’d slap down Maxwell’s equations and the Lorentz transformations too, but…meh. Enough intellectual boasting for one day. It doesn’t bring in the chicks.

Sadly, except for the rectangular moment of inertia formula and bending/shear stress, this is the only place I’ve ever had to use any of these equations in my post-collegate career. Why, exactly, did I leave school? :dubious:

Stranger

1. Okay, I checked these to make sure I got them right…but I did.

Well, all of the chemistry equations note and a few of the physics ones plus one I thought I’d never used after college:

Half Life Decay

(Activity at Calibration)=(Activity at assay)e^-ln2( t)/(half life)

Oh and G= H-T S

All s represent Deltas.

That one’s not only burned into my brain, it’s burned onto my arm. You can get a tattoo of just about anything these days.

Except, like all normal human beings, I use i for the imaginary unit, not j. What are you, an electrician or something?

WORM: Width Over Range x Mils

Not a science or math geek at all, but for some reason, like David Simmons, I have Avagadro’s Number etched permanently into my brain. 6.02 x 10[sup]23[/sup]. Like I’m ever going to use that!

I’m afraid the equations stuck in my head greatly exceed my ability to enter Greek subscripts. I’ll give Stranger credit for having a few stuck in his head that I have somehow dislodged. To give a taste for what clutters my mind, I not only have the equations of General Relativity stuck in my head, I have various related equations, such as the metric in the Schwarzschild spacetime, the definition of the Lie derivitive, and all sorts of fun stuff that impresses so many at parties.

I’ve wired a few electric chairs in my time.

Come on in, have a seat. Seriously, everybody in my Physics program was double majoring in EE (before we all dispersed into seperate departments), and so j became the way to express the imaginary number. Oddly enough, it was also used in my Design of Machinery (mechanism design) class for polar vectors. In all other places, though, i sufficed, but it sort of stuck with me.

Stranger

Some of the above, along with:

C=λf

(velocity = wavelength x frequency)

And Snell’s law:

n[sub]1[/sub]sinΘ[sub]1[/sub] = n[sub]2[/sub]sinΘ[sub]2[/sub]

where n=refraction index

Slope:

y=mx+b

Law of Cosines:

c2 = a2 + b2 - (2)(a)(b)(cos X)

From that you can derive whatever else you’ll need to fix a geometry problem.

Pythagorean theorem:

c[sup]2[/sup] = a[sup]2[/sup] + b[sup]2[/sup]

Acoustic Impedance:

Density x Velocity = AI

Reflection Coefficient:

(**ρ[sub]2[/sub]*v[sub]2[/sub]+ρ[sub]1[/sub]*v[sub]1[/sub])/ρ[sub]2[/sub]v[sub]2[/sub]+ρ[sub]1[/sub]v[sub]1[/sub])

It seems like a paltry collection, but I maintain a small library of reference materials at work, and that with the above allows me to be a performing geoscientist.

Assets = Liabilities + Equity

Wow… feeling a bit overmatched in the equations displayed here but here’s one I always remember for some reason.

N = R* × fp × ne × fl × fi × fc × L

which is Drake’s Equation, known and beloved (or derided) by geeks everywhere. :>

What, no one mentioned Sin^2 + Cos^2 = 1

I will NEVER forget this damn equation.
because my algebra II teacher sang it, endlessly, to the tune of “All Around the Mulberry Bush” (or whatever the hell it’s called), and made us do so as well.

it drove me bats, but it fuckin’ worked…

E = MC^2

The only equation I’ve never had to use in Physics :mad: . It just always pops into my head anytime I hear about spaceships (in sci-fi) and their limitations.