A Cylindrical Particle Model
An atomic event modeled as a geometric cylinder in Euclidean space.
An atomic event modeled as a geometric cylinder in Euclidean space.

Consider an excited atomic particle P described by a repetitive chain of events

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1} , \sf{\Omega}_{2}, \sf{\Omega}_{3} \ \ldots \ \right)$

where each repeated cycle $\sf{\Omega}$ is a space-time event. Let this particle be characterized by its orbital radius $R$ and wavelength $\lambda$. These properties are related to position in a Euclidean space. And we can use them to make a simple geometric model of P that is shaped like a cylinder. Or to be more exact; like a finite section of a right circular cylinder with its ends closed to form two circular surfaces, oriented along the $z$-axis, similar to the one shown in the accompanying diagram. Defintion: the area of the circular cross section is

$A \equiv \pi R ^{ 2}$

This is just a statement of ancient knowledge about circles going back at least to ArchimedesXlink.png. And to restate another traditionalXlink.png mensuration formula, the volume of the cylinder is

$V \equiv \lambda A = \lambda \pi R^{2}$

We use this model to visualize one atomic event. Then it is easy to imagine the chain of events $\Psi$ as a row of cylinders strung-out end-to-end, like a tube or wire.

Right.png Next step: Euclidean space.
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