$$2\cdot 4\cdot 6\cdot\ldots\cdot(2n)=2^nn!$$ How it can be seen in a plane? I have found many proofs with by induction but I wish to understand it geometrically.

A dual number is a number of the form $a+b\varepsilon$, where $a,b \in \mathbb{R}$ and $\varepsilon$ is a nonreal number with the property $\varepsilon^2=0$. Dual numbers are in some ways similar to the complex numbers $a+bi$, where $i^2=-1$. Complex numbers have a very elegant geometric interpretation. Specifically, we can treat complex numbers as vectors in […]

As in the title, I was wondering if the formula: $$a\times (b\times c)=b(a\cdot c)-c(a \cdot b)$$ for $\mathbb R ^3$ cross product has some geometrical interpretation. I’ve recently seen a proof (from Vector Analysis – J.W. Gibbs) that’s not at all difficult to understand, however I would hardly remember the steps of the proof (and […]

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