If I draw 2 perpendicular line segments on the ground, 3 meters and 4 meters, how far into the sky does their cross-product extend? What if instead the line lengths are 300 cm and 400 cm? Can someone explain cross-products to me in a way that won’t make Pythagoras angry?

What are units (like meters $m$, seconds $s$, kilogram $kg$, …) from a mathematical point of view? I’ve made the observation that units “behave like numbers”. For example, we can divide them (as in $m/s$, which is a unit of speed), and also square them (the unit of acceleration is $\frac{m}{s^2}$). In addition to that, […]

I know there are higher dimensional analogues of the argument principle. (See http://en.wikipedia.org/wiki/Variation_of_argument) But I do not have books about it and I cannot find anything of value on the internet for free. Plz give me references or explainations. I would like an example of how one can find the zero’s of functions in 3 […]

Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit. For all other cases, you need to introduce the unit conversion fraction, and cancel explicitly. Is it because radians and angles have no relevance to linear speed (v), so they are simply discarded?

In physics we deal with quantities which have a magnitude and a unit type, such as 4m, 9.8 m/s², and so forth. We might represent these as elements of $\Bbb R\times \Bbb Q^n$ (where there are $n$ different fundamental units), with $(4, \langle1,0,0\rangle)$ representing 4m, $(9.8, \langle1,0,-2\rangle)$ representing 9.8 m s⁻², and so forth, with […]

Intereting Posts

Inequality on a general convex normed space
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
Integral $\int_0^{\pi/2}\arctan^2\left(\frac{6\sin x}{3+\cos 2x}\right)\mathrm dx$
Does $a!b!$ always divide $(a+b)!$
What do people mean by “finite”?
Solve $x(x+1)=y(y+1)(y^2+2)$ for $x,y$ over the integers
Holder's inequality $ \sum_{i=1}^n |u_i v_i| \leq (\sum_{i=1}^n |u_i|^p )^{\frac{1}{p}}(\sum_{i=1}^n |v_i|^q )^\frac{1}{q} $
Prove two reflections of lines through the origin generate a dihedral group.
What is the relationship between base and number of digits?
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
Question about entropy
Integrating: $\int_0^\infty \frac{\sin (ax)}{e^x + 1}dx$
Proof that continuous partial derivatives implies differentiability
Fourier Inversion formula on $L^2$