# I am a shape and yet I'm a letter

I take direction and help find density.

I am the graph of a function where none of it is negative.

But I am not used to make equations

Nor am I one to raise to power.

What am I?

You are

V

I am a shape and yet I'm a letter

V is a letter, and it can describe a shape, e.g. migrating birds fly in a V-shape.

I take direction and help find density.

V points downwards. It's in the denominator of the formula for density, $\rho=\frac mV$.

I am the graph of a function where none of it is negative.

The graph of the absolute-value function is shaped like a V.

But I am not used to make equations
Nor am I one to raise to power.

It's not <,> or ^.

• I interpreted "I take direction" as v being the mathematical symbol for velocity, which is a vector (i.e. velocity having both speed and direction) Jul 24, 2016 at 14:03
• I don't quite understand why V can't be part of an equation. In fact, it is in the formula for density. Jul 25, 2016 at 3:34
• @KevinOrr "<>" is used to write equations. Its a latex syntax. Jul 25, 2016 at 4:26
• For I take direction, could it be because of V sounds like "way"? And I am not very much to the explanation "...fly V-shape", what about "W-shape" and "X-shape", every letter can be a shape this way. Jul 25, 2016 at 6:45
• inequation, an equation is just the opposite. I was confused by this, too. Many languages (LaTeX, SQL, Pascal, ...) use <> as not equal. Jul 25, 2016 at 11:12

Are you

Mass, $m$

I am a shape and yet I'm a letter

Every mass has a shape and is represented by $m$.

I take direction and help find density.

Mass can be given a direction by a velocity vector, etc. $Density$ $= \frac{mass}{volume}$.

I am the graph of a function where none of it is negative.

All values of a probability mass function must be positive.

But I am not used to make equations

$m$ is generally not the variable in an equation. For instance, in graphing kinetic energy the velocity is the variable of concern.

Nor am I one to raise to power.

I can't think of where mass is squared or cubed...but I'm really tired right now.

• Good, but doubt it's right as m is definitely used in the equation e=mc2 Jul 25, 2016 at 13:42

Are you

Volume

I am a shape and yet I'm a letter

Volume is a shape, and a volume (drive) on a computer is usually designated by a letter

I take direction and help find density.

Volume (of a radio for example) can go up and down, and density is found by dividing mass by volume

I am the graph of a function where none of it is negative.

I'm thinking this could be related to integrals (in 2D space this would be Area, but this must be 3D space?

But I am not used to make equations

Rules out any operators, volume itself isn't used to make equations

Nor am I one to raise to power.

Rules out ^ as the answer

I don't like my chances here, the explanations aren't really that solid.

Long shot the letter I (capital i)

I take direction and help find density.

The I is basicly a line, the equation

   m
p=---
v


has a line in the center (it's a I rotated 90 degrees), it takes direction by the order of m/v if you change m/v from position the direction of the formula changes.

I know it does not answer multiple questions (yet) but the reason I belive it's the I:

I take direction and help find density.

I am the graph of a function where none of it is negative.

But I am not used to make equations

Nor am I one to raise to power. What am I?